This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topol...This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topologies.In comparison with the previous achievements on formation control problems,the UAV swarm system with Lipschitz nonlinear dynamics can accomplish the pre-designed TVF while tracking a pre-given trajectory which is produced by a virtual leader UAV in the presence of external disturbances.Firstly,by applying the consensus theory,a TVF controller is developed with the local neighborhood status information,the errors of real time status of all UAVs,the expected formation configuration and the pre-given trajectory under directed switching topologies.Secondly,through a certain matrix variable substitution,the UAV swarm system formation control issue is transformed into a lower dimensional asymptotically stable control issue.Thirdly,by introducing the minimum dwell time,the design steps of formation control algorithm are further acquired.In the meantime,the stability of the UAV swarm system is analyzed through the construction of a piecewise continuous Lyapunov functional and via the Linear Matrix Inequalities(LMIs)method.Finally,the comparison results of a numerical simulation are elaborated to verify the validity of the proposed approach.展开更多
The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital ...The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.展开更多
Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coup...Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.展开更多
An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this pa...An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.展开更多
Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with r...Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with rigid water hammer and hydro-turbine generator unit(HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient eis variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast–slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values.展开更多
Data-driven reduced-order modeling opens new avenues of understanding,predicting,controlling,and optimizing system behavior.Simple systems may have state spaces in which sparse human-interpretable dynamical systems ca...Data-driven reduced-order modeling opens new avenues of understanding,predicting,controlling,and optimizing system behavior.Simple systems may have state spaces in which sparse human-interpretable dynamical systems can be identified.This approach has been pioneered by Brunton et al.(2016,PNAS)with sparse identification of nonlinear dynamics.Complex systems,however,cannot be expected to benefit from such simple analytical descriptions.Yet,smoothness may be exploited by analytical local descriptions.In this paper,we identify a clusterwise polynomial dynamics from time-resolved snapshot data.The full state space is partitioned into clusters with a reduced-order polynomial description for each cluster and a global patching strategy.The resulting clusterwise modeling is entirely data-driven and requires no prior knowledge of the system dynamics.We illustrate the approach on the well-known chaotic Lorenz and Rössler systems,on the more challenging chaotic fluid flow dynamics of higher state-space dimensions,on a noisy electrocardiogram signal,and finally on the time evolution of the monthly sunspot number.Clusterwise modeling offers a powerful and interpretable paradigm for dynamical modeling.Nonlinear dynamics can be approximated by assembling many simple local models of different resolutions,opening new paths to understand and control intricate nonlinearities.展开更多
In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical a...In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.展开更多
The design and optimization of nonlinear fiber laser sources,such as soliton self-frequency shift(SSFS)tunable sources and supercontinuum(SC)sources,have traditionally relied on manual tuning and simulations,posing ch...The design and optimization of nonlinear fiber laser sources,such as soliton self-frequency shift(SSFS)tunable sources and supercontinuum(SC)sources,have traditionally relied on manual tuning and simulations,posing challenges for real-time applications.Machine learning has shown promise in fiber nonlinear propagation characterization,but the optimization and design of nonlinear systems remain relatively unexplored,especially under multitarget optimization conditions.In this paper,we propose a method that combines deep reinforcement learning(DRL)and deep neural network(DNN)to achieve fast synchronization optimization of ultrafast pulse nonlinear propagation in optical fibers under multitarget optimization tasks,with applications demonstrated in complex SSFS and SC generation systems in the mid-infrared band.The results indicate that a set of optimization parameters can be obtained in a few seconds,enabling rapid,automated tuning of pulse parameters in pursuit of diverse optimization objectives.This integration of DRL and DNN models holds transformative potential for the real-time optimization of not only fiber lasers but also a wide variety of complex photonic systems,paving the way for intelligent,adaptive optical system design and operation.展开更多
Sparse identification of nonlinear dynamics(SINDy)has made significant progress in data-driven dynamics modeling.However,determining appropriate hyperparameters and addressing the time-consuming symbolic regression pr...Sparse identification of nonlinear dynamics(SINDy)has made significant progress in data-driven dynamics modeling.However,determining appropriate hyperparameters and addressing the time-consuming symbolic regression process remain substantial challenges.This study proposes the adaptive backward stepwise selection of fast SINDy(ABSS-FSINDy),which integrates statistical learning-based estimation and technical advancements to significantly reduce simulation time.This approach not only provides insights into the conditions under which SINDy performs optimally but also highlights potential failure points,particularly in the context of backward stepwise selection(BSS).By decoding predefined features into textual expressions,ABSS-FSINDy significantly reduces the simulation time compared with conventional symbolic regression methods.We validate the proposed method through a series of numerical experiments involving both planar/spatial dynamics and high-dimensional chaotic systems,including Lotka-Volterra,hyperchaotic Rossler,coupled Lorenz,and Lorenz 96 benchmark systems.The experimental results demonstrate that ABSS-FSINDy autonomously determines optimal hyperparameters within the SINDy framework,overcoming the curse of dimensionality in high-dimensional simulations.This improvement is substantial across both lowand high-dimensional systems,yielding efficiency gains of one to three orders of magnitude.For instance,in a 20D dynamical system,the simulation time is reduced from 107.63 s to just 0.093 s,resulting in a 3-order-of-magnitude improvement in simulation efficiency.This advancement broadens the applicability of SINDy for the identification and reconstruction of high-dimensional dynamical systems.展开更多
This study describes a new solution for resolving nonlinear dynamics. Surpri<span>singly, it has been resolved and completed by non-physicists on behalf of</span> phy<span>sicists in 2021. It is a re...This study describes a new solution for resolving nonlinear dynamics. Surpri<span>singly, it has been resolved and completed by non-physicists on behalf of</span> phy<span>sicists in 2021. It is a revolutionary solution like the Copernican Theory,</span> which is perfectly different from the existing chaos theory. In the past, nonlinear <span>dynamics has been analyzed using logical solutions, such as chaos theory,</span> based on logical thinking. However, it is not perfect systematic solution, hence;the new solution has been analyzed and resolved by systematic analytical tool in other sciences. Then, the result is more perfect and precise than the old chaos theory. Regrettably, most physicists do not welcome this advancement, because they have primitive solutions such as chaos theory. If the new solution <span>is true, it is very disadvantageous to them like Galileo’s heliocentric theory. Therefore, they do not welcome it and deny and reject it. Hence, they wish it to fail;moreover, they want to remain in safe zone. Unfortunately, they became outsiders because they have no ability to review new solutions. Unfortunately, we have no obligation to follow physicists. If so, non-physicists, bypassing physicists, must study independently nonlinear dynamics based on systems thinking, and have to share the findings</span></span><span style="font-family:""> </span><span style="font-family:"">other</span><span style="font-family:""> </span><span style="font-family:"">scientists. It means that</span><span style="font-family:""> <span>the new solution would be replaced the chaos theory in traditional physics;moreover, it would be resolved many unsolved nonlinear dynamics in the fu</span>ture.展开更多
Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amp...Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amphibious vehicle is established.The Hamiltonian function of the nonlinear rolling dynamical equation of amphibious vehicle indicate when subjected to joint action of periodic wave excitation and crosswind,the nonlinear rolling system degenerates into being asymmetric.The threshold value of excited moment of wave and wind is analyzed by the Melnikov method.Finally,the nonlinear rolling motion response and phase portrait were simulated by four order Runge-Kutta method at different excited moment parameters.展开更多
This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is ca...This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincaré map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable re- lationship between the dual-frequency excitations.展开更多
Aero-engine rotor systems installed in aircraft are considered to have a base motion.In this paper,a flexible asymmetric rotor system is modeled considering the nonlinear supports of ball bearings and Squeeze Film Dam...Aero-engine rotor systems installed in aircraft are considered to have a base motion.In this paper,a flexible asymmetric rotor system is modeled considering the nonlinear supports of ball bearings and Squeeze Film Dampers(SFDs),and the dynamic characteristics of the rotor system under maneuvering flight are systematically studied.Effects of the translational accelerative motions,the angular motions and the pitching flight with combined translational and angular motions on nonlinear dynamic behavior of the rotor system are investigated.The results show that,due to the nonlinear coupled effects among the rotor,ball bearings and SFDs,within the first bending resonance region,responses of the rotor show obvious nonlinear characteristics such as bistable phenomenon,amplitude jumping phenomenon and non-synchronous vibration.Translational acceleration motion of the aircraft leads to axis offset of the rotor system and thus results in the reduction and the final disappearance of the bistable rotating speed region.The pitching angular motion mainly affects rotational vibration of the rotor system,and thus further induces their transverse vibrations.For the pitching flight with combined translational and angular motions,a critical flight parameter is found to correspond to the conversion of two steady responses of the rotor system,in which one response displays small amplitude and synchronous vibration,and the other shows large amplitude and non-synchronous vibration.展开更多
The nonlinear dynamic behaviors of flexible rotor system with hydrodynamicbearing supports are analyzed. The shaft is modeled by using the finite element method that takesthe effect of inertia and shear into considera...The nonlinear dynamic behaviors of flexible rotor system with hydrodynamicbearing supports are analyzed. The shaft is modeled by using the finite element method that takesthe effect of inertia and shear into consideration. According to the nonlinearity of thehydrodynamic journal bearing-flexible rotor system, a modified modal synthesis technique withfree-interface is represented to reduce degrees-of-freedom of model of the flexible rotor system.According to physical character of oil film, variational constrain approach is introduced tocontinuously revise the variational form of Reynolds equation at every step of dynamic integrationand iteration. Fluid lubrication problem with Reynolds boundary is solved by the isoparametricfinite element method without the increasing of computing efforts. Nonlinear oil film forces andtheir Jacobians are simultaneously calculated and their compatible accuracy is obtained. Theperiodic motions are obtained by using the Poincare -Newton-Floquet (PNF) method. A method,combining the predictor-corrector mechanism to the PNF method, is presented to calculate thebifurcation point of periodic motions to be subject to change of system parameters. The localstability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The chaoticmotions of the bearing-rotor system are investigated by power spectrum. The numerical examples showthat the scheme of this study saves computing efforts but also is of good precision.展开更多
This paper considers the dynamical behavior of a Duffing-Mathieu type system with a cubic single-well potential during the principal parametric resonance. Both the cases of constant and time-dependent excitation ampli...This paper considers the dynamical behavior of a Duffing-Mathieu type system with a cubic single-well potential during the principal parametric resonance. Both the cases of constant and time-dependent excitation amplitude are used to observe the variation of the extent and the rate of the erosion in safe basins. It is evident that the appearance of fractal basin boundaries heralds the onset of the losing of structural integrity. The minimum value of control parameter to prevent the basin from erosion is given along with the excitation amplitude varying. The results show the time-dependence of excitation amplitude can be used to control the extent and the rate of the erosion and delay the first occurrence of heteroclinic tangency.展开更多
In this paper we study the dynamic properties and stabilities of neural networks with delay-time (which includes the time-varying case) by differential inequalities and Lyapunov function approaches. The criteria of co...In this paper we study the dynamic properties and stabilities of neural networks with delay-time (which includes the time-varying case) by differential inequalities and Lyapunov function approaches. The criteria of connective stability, robust stability, Lyapunov stability, asymptotic atability, exponential stability and Lagrange stability of neural networks with delay-time are established, and the results obtained are very useful for the design, implementation and application of adaptive learning neural networks.展开更多
In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration...In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.展开更多
This paper is concerned with the recursive filtering problem for a class of discrete-time nonlinear stochastic systems in the presence of multi-sensor measurement delay. The delay occurs in a multi-step and asynchrono...This paper is concerned with the recursive filtering problem for a class of discrete-time nonlinear stochastic systems in the presence of multi-sensor measurement delay. The delay occurs in a multi-step and asynchronous manner, and the delay probability of each sensor is assumed to be known or unknown. Firstly, a new model is constructed to describe the measurement process, based on which a new particle filter is developed with the ability to fuse multi-sensor information in the case of known delay probability.In addition, an online delay probability estimation module is introduced in the particle filtering framework, which leads to another new filter that can be implemented without the prior knowledge of delay probability. More importantly, since there is no complex iterative operation, the resulting filter can be implemented recursively and is suitable for many real-time applications. Simulation results show the effectiveness of the proposed filters.展开更多
This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The pap...This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demoastrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time （MECT） and optimal step-size （OS）. In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.展开更多
The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activa...The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-com- puting is a practical and advanced tool for solving large-scale underground rock engineering problems.展开更多
基金co-supported by the Key-area Research and Development Program of Guangdong ProvinceChina(No.2019B090915001)+2 种基金National Key R&D Program of China(No.2018YFB1308000),National Natural Science Funds of China(Nos.61772508,U1913202,U1813205,U1713213)CAS Key Technology Talent Program,Shenzhen Technology ProjectChina(Nos.JCYJ20180507182610734,JSGG20191129094012321).
文摘This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topologies.In comparison with the previous achievements on formation control problems,the UAV swarm system with Lipschitz nonlinear dynamics can accomplish the pre-designed TVF while tracking a pre-given trajectory which is produced by a virtual leader UAV in the presence of external disturbances.Firstly,by applying the consensus theory,a TVF controller is developed with the local neighborhood status information,the errors of real time status of all UAVs,the expected formation configuration and the pre-given trajectory under directed switching topologies.Secondly,through a certain matrix variable substitution,the UAV swarm system formation control issue is transformed into a lower dimensional asymptotically stable control issue.Thirdly,by introducing the minimum dwell time,the design steps of formation control algorithm are further acquired.In the meantime,the stability of the UAV swarm system is analyzed through the construction of a piecewise continuous Lyapunov functional and via the Linear Matrix Inequalities(LMIs)method.Finally,the comparison results of a numerical simulation are elaborated to verify the validity of the proposed approach.
基金supported by the National Natural Science Foundation of China(Nos.11002068 and11202094)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(No.0113Y01)the Priority Academic Program of Jiangsu Higher Education Institutions
文摘The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.
基金supported by the National Key Research and Development Program of China(No.2022YFB3203600)the National Natural Science Foundation of China(Nos.12202355,12132013,and 12172323)the Zhejiang Provincial Natural Science Foundation of China(No.LZ22A020003)。
文摘Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.
基金the National Natural Science Foundation of China(Nos.11772293 and12072312)Zhejiang Science and Technology Project(No.2019C03129)。
文摘An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.
基金Project supported by the National Natural Science Foundation of China for Outstanding Youth(Grant No.51622906)the National Natural Science Foundation of China(Grant No.51479173)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.201304030577)the Scientific Research Funds of Northwest A&F University(Grant No.2013BSJJ095)the Science Fund for Excellent Young Scholars from Northwest A&F University and Shaanxi Nova Program,China(Grant No.2016KJXX-55)
文摘Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with rigid water hammer and hydro-turbine generator unit(HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient eis variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast–slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values.
基金supported by the National Natural Science Foundation of China(Grant Nos.12172109,12202121,and 12302293)the China Postdoctoral Science Foundation(Grant Nos.2023M730866 and 2023T160166)+1 种基金the Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515011492)the Shenzhen Science and Technology Program(Grant Nos.JCYJ20220531095605012,KJZD20230923115210021,and 29853MKCJ202300205).
文摘Data-driven reduced-order modeling opens new avenues of understanding,predicting,controlling,and optimizing system behavior.Simple systems may have state spaces in which sparse human-interpretable dynamical systems can be identified.This approach has been pioneered by Brunton et al.(2016,PNAS)with sparse identification of nonlinear dynamics.Complex systems,however,cannot be expected to benefit from such simple analytical descriptions.Yet,smoothness may be exploited by analytical local descriptions.In this paper,we identify a clusterwise polynomial dynamics from time-resolved snapshot data.The full state space is partitioned into clusters with a reduced-order polynomial description for each cluster and a global patching strategy.The resulting clusterwise modeling is entirely data-driven and requires no prior knowledge of the system dynamics.We illustrate the approach on the well-known chaotic Lorenz and Rössler systems,on the more challenging chaotic fluid flow dynamics of higher state-space dimensions,on a noisy electrocardiogram signal,and finally on the time evolution of the monthly sunspot number.Clusterwise modeling offers a powerful and interpretable paradigm for dynamical modeling.Nonlinear dynamics can be approximated by assembling many simple local models of different resolutions,opening new paths to understand and control intricate nonlinearities.
基金supported by the National Natural Science Foundation of China(Nos.52401342 and 12572025)the Fundamental Research Funds for the Central Universities of China(Nos.D5000240076 and G2025KY05171)+1 种基金the Natural Science Basic Research Program of Shaanxi Province(No.2025JCYBMS-026)the Basic Research Programs of Taicang(No.TC2024JC36)。
文摘In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.
基金supported by the National Natural Science Foundation of China(Grant No.62575051)the Aeronautical Science Foundation of China(Grant No.2023M038080001)+1 种基金the Equipment Pre-research Joint Fund of the Ministry of Education(Grant No.8091B042228)the Science and Technology Project of Sichuan Province(Grant Nos.2023NSFSC1964 and 203NSFSC0033).
文摘The design and optimization of nonlinear fiber laser sources,such as soliton self-frequency shift(SSFS)tunable sources and supercontinuum(SC)sources,have traditionally relied on manual tuning and simulations,posing challenges for real-time applications.Machine learning has shown promise in fiber nonlinear propagation characterization,but the optimization and design of nonlinear systems remain relatively unexplored,especially under multitarget optimization conditions.In this paper,we propose a method that combines deep reinforcement learning(DRL)and deep neural network(DNN)to achieve fast synchronization optimization of ultrafast pulse nonlinear propagation in optical fibers under multitarget optimization tasks,with applications demonstrated in complex SSFS and SC generation systems in the mid-infrared band.The results indicate that a set of optimization parameters can be obtained in a few seconds,enabling rapid,automated tuning of pulse parameters in pursuit of diverse optimization objectives.This integration of DRL and DNN models holds transformative potential for the real-time optimization of not only fiber lasers but also a wide variety of complex photonic systems,paving the way for intelligent,adaptive optical system design and operation.
基金Project supported by the National Natural Science Foundation of China(Nos.12172291,12472357,and 12232015)the Shaanxi Province Outstanding Youth Fund Project(No.2024JC-JCQN-05)the 111 Project(No.BP0719007)。
文摘Sparse identification of nonlinear dynamics(SINDy)has made significant progress in data-driven dynamics modeling.However,determining appropriate hyperparameters and addressing the time-consuming symbolic regression process remain substantial challenges.This study proposes the adaptive backward stepwise selection of fast SINDy(ABSS-FSINDy),which integrates statistical learning-based estimation and technical advancements to significantly reduce simulation time.This approach not only provides insights into the conditions under which SINDy performs optimally but also highlights potential failure points,particularly in the context of backward stepwise selection(BSS).By decoding predefined features into textual expressions,ABSS-FSINDy significantly reduces the simulation time compared with conventional symbolic regression methods.We validate the proposed method through a series of numerical experiments involving both planar/spatial dynamics and high-dimensional chaotic systems,including Lotka-Volterra,hyperchaotic Rossler,coupled Lorenz,and Lorenz 96 benchmark systems.The experimental results demonstrate that ABSS-FSINDy autonomously determines optimal hyperparameters within the SINDy framework,overcoming the curse of dimensionality in high-dimensional simulations.This improvement is substantial across both lowand high-dimensional systems,yielding efficiency gains of one to three orders of magnitude.For instance,in a 20D dynamical system,the simulation time is reduced from 107.63 s to just 0.093 s,resulting in a 3-order-of-magnitude improvement in simulation efficiency.This advancement broadens the applicability of SINDy for the identification and reconstruction of high-dimensional dynamical systems.
文摘This study describes a new solution for resolving nonlinear dynamics. Surpri<span>singly, it has been resolved and completed by non-physicists on behalf of</span> phy<span>sicists in 2021. It is a revolutionary solution like the Copernican Theory,</span> which is perfectly different from the existing chaos theory. In the past, nonlinear <span>dynamics has been analyzed using logical solutions, such as chaos theory,</span> based on logical thinking. However, it is not perfect systematic solution, hence;the new solution has been analyzed and resolved by systematic analytical tool in other sciences. Then, the result is more perfect and precise than the old chaos theory. Regrettably, most physicists do not welcome this advancement, because they have primitive solutions such as chaos theory. If the new solution <span>is true, it is very disadvantageous to them like Galileo’s heliocentric theory. Therefore, they do not welcome it and deny and reject it. Hence, they wish it to fail;moreover, they want to remain in safe zone. Unfortunately, they became outsiders because they have no ability to review new solutions. Unfortunately, we have no obligation to follow physicists. If so, non-physicists, bypassing physicists, must study independently nonlinear dynamics based on systems thinking, and have to share the findings</span></span><span style="font-family:""> </span><span style="font-family:"">other</span><span style="font-family:""> </span><span style="font-family:"">scientists. It means that</span><span style="font-family:""> <span>the new solution would be replaced the chaos theory in traditional physics;moreover, it would be resolved many unsolved nonlinear dynamics in the fu</span>ture.
基金The Pre-research Project of the General Armament DepartmentThe Science Fund of North University of China(No.20130105)
文摘Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amphibious vehicle is established.The Hamiltonian function of the nonlinear rolling dynamical equation of amphibious vehicle indicate when subjected to joint action of periodic wave excitation and crosswind,the nonlinear rolling system degenerates into being asymmetric.The threshold value of excited moment of wave and wind is analyzed by the Melnikov method.Finally,the nonlinear rolling motion response and phase portrait were simulated by four order Runge-Kutta method at different excited moment parameters.
基金Project supported by the State Key Program of National Natural Science Foundation of China(No.11232009)the National Natural Science Foundation of China(Nos.11372171 and 11422214)
文摘This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincaré map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable re- lationship between the dual-frequency excitations.
基金the National Key Basic Research Program of China(No.2015CB057400)the National Natural Science Foundation of China(Nos.11672201 and 11872045)the Major Special Basic Research Projects for Aeroengines and Gas Turbines(No.2017-IV-0008-0045)。
文摘Aero-engine rotor systems installed in aircraft are considered to have a base motion.In this paper,a flexible asymmetric rotor system is modeled considering the nonlinear supports of ball bearings and Squeeze Film Dampers(SFDs),and the dynamic characteristics of the rotor system under maneuvering flight are systematically studied.Effects of the translational accelerative motions,the angular motions and the pitching flight with combined translational and angular motions on nonlinear dynamic behavior of the rotor system are investigated.The results show that,due to the nonlinear coupled effects among the rotor,ball bearings and SFDs,within the first bending resonance region,responses of the rotor show obvious nonlinear characteristics such as bistable phenomenon,amplitude jumping phenomenon and non-synchronous vibration.Translational acceleration motion of the aircraft leads to axis offset of the rotor system and thus results in the reduction and the final disappearance of the bistable rotating speed region.The pitching angular motion mainly affects rotational vibration of the rotor system,and thus further induces their transverse vibrations.For the pitching flight with combined translational and angular motions,a critical flight parameter is found to correspond to the conversion of two steady responses of the rotor system,in which one response displays small amplitude and synchronous vibration,and the other shows large amplitude and non-synchronous vibration.
基金This project is supported by National Natural Science Foundation of China (No.50275116) National 863 of China(No.2002AA414060, No.2002AA-503020).
文摘The nonlinear dynamic behaviors of flexible rotor system with hydrodynamicbearing supports are analyzed. The shaft is modeled by using the finite element method that takesthe effect of inertia and shear into consideration. According to the nonlinearity of thehydrodynamic journal bearing-flexible rotor system, a modified modal synthesis technique withfree-interface is represented to reduce degrees-of-freedom of model of the flexible rotor system.According to physical character of oil film, variational constrain approach is introduced tocontinuously revise the variational form of Reynolds equation at every step of dynamic integrationand iteration. Fluid lubrication problem with Reynolds boundary is solved by the isoparametricfinite element method without the increasing of computing efforts. Nonlinear oil film forces andtheir Jacobians are simultaneously calculated and their compatible accuracy is obtained. Theperiodic motions are obtained by using the Poincare -Newton-Floquet (PNF) method. A method,combining the predictor-corrector mechanism to the PNF method, is presented to calculate thebifurcation point of periodic motions to be subject to change of system parameters. The localstability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The chaoticmotions of the bearing-rotor system are investigated by power spectrum. The numerical examples showthat the scheme of this study saves computing efforts but also is of good precision.
基金the National Science Foundation of ChinaPSF of China
文摘This paper considers the dynamical behavior of a Duffing-Mathieu type system with a cubic single-well potential during the principal parametric resonance. Both the cases of constant and time-dependent excitation amplitude are used to observe the variation of the extent and the rate of the erosion in safe basins. It is evident that the appearance of fractal basin boundaries heralds the onset of the losing of structural integrity. The minimum value of control parameter to prevent the basin from erosion is given along with the excitation amplitude varying. The results show the time-dependence of excitation amplitude can be used to control the extent and the rate of the erosion and delay the first occurrence of heteroclinic tangency.
文摘In this paper we study the dynamic properties and stabilities of neural networks with delay-time (which includes the time-varying case) by differential inequalities and Lyapunov function approaches. The criteria of connective stability, robust stability, Lyapunov stability, asymptotic atability, exponential stability and Lagrange stability of neural networks with delay-time are established, and the results obtained are very useful for the design, implementation and application of adaptive learning neural networks.
基金Project supported by the National Natural Science Foundation of China(Nos.11172107 and 11172109)the Program for New Century Excellent Talents in University(No.NCET-11-0183)
文摘In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.
基金supported by the National Natural Science Foundation of China(6147322711472222)+3 种基金the Fundamental Research Funds for the Central Universities(3102015ZY001)the Aerospace Technology Support Fund of China(2014-HT-XGD)the Natural Science Foundation of Shaanxi Province(2015JM6304)the Aeronautical Science Foundation of China(20151353018)
文摘This paper is concerned with the recursive filtering problem for a class of discrete-time nonlinear stochastic systems in the presence of multi-sensor measurement delay. The delay occurs in a multi-step and asynchronous manner, and the delay probability of each sensor is assumed to be known or unknown. Firstly, a new model is constructed to describe the measurement process, based on which a new particle filter is developed with the ability to fuse multi-sensor information in the case of known delay probability.In addition, an online delay probability estimation module is introduced in the particle filtering framework, which leads to another new filter that can be implemented without the prior knowledge of delay probability. More importantly, since there is no complex iterative operation, the resulting filter can be implemented recursively and is suitable for many real-time applications. Simulation results show the effectiveness of the proposed filters.
基金This study was supported by the National Key Basic Research and Development Project of China 2004CB418303 the National Natural Science foundation of China under Grant Nos. 40305012 and 40475027Jiangsu Key Laboratory of Meteorological Disaster KLME0601.
文摘This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demoastrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time （MECT） and optimal step-size （OS）. In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.
基金This work was financially supported by the Key Project for National Science of "9.5" (Reward Ⅱ for National Science and Technol
文摘The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-com- puting is a practical and advanced tool for solving large-scale underground rock engineering problems.
