A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. B...A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.展开更多
We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species or prey, and a type III Holling functional response for the middle ...We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species or prey, and a type III Holling functional response for the middle and highest trophic species (first and second predator respectively). We prove that this model exhibits two small amplitud periodic solutions bifurcating simultaneously each one from one of the two zero-Hopf equilibrium points that the model has adequate values of its parameters. As far as we know, this is the first time that the phenomena appear in the literature related with food chain models.展开更多
The bifurcation of the second-order approximate solutions of nonlinear parametrically excited systems possessing generalized van der Pol's dampings and quintic Duffing's nonlinearities subjected to a primary p...The bifurcation of the second-order approximate solutions of nonlinear parametrically excited systems possessing generalized van der Pol's dampings and quintic Duffing's nonlinearities subjected to a primary parametric resonance is investigated. Using singularity theory with Z2-symmetry, bifurcations of the solutions are universally classified in a topologically equivalent sense for Z2-codimension>3. The question of whether the approximate solutions from the classical perturbation methods can be topologically equivalent in describing the periodic responses and the bifurcations of the original systems is made clear. The numerical results indicate that the vibration characteristic may suddenly disappear in the range of Z2-codimension>4.展开更多
In this study the Zweifach-Fung effect is investigated in a Y-shaped bifurcation when the clearance between the rigid spherical particle and the walls is small compared to both channel’s and particle’s radii.Single-...In this study the Zweifach-Fung effect is investigated in a Y-shaped bifurcation when the clearance between the rigid spherical particle and the walls is small compared to both channel’s and particle’s radii.Single-and two-particle systems are studied using resolved computational fluid dynamics coupled to discrete element method to obtain a two-dimensional map of the initially positioned particles that would enter each child branch.In all cases,the path selection of the sphere depends on its two-dimensional positioning far from the bifurcation region in the parent channel.Increasing the flow rate ratio or decreasing the Reynolds number intensifies the Zweifach-Fung bifurcation effect in a single-particle system.Similarly,in two-particle systems where non-contact particle-particle interaction is present,decreasing the particle-to-particle distance reduces the bifurcation effect,while changing the Reynolds number has the same influence as in the single-particle systems.The results provide insight for optimizing the flow characteristics in bifurcating microchannels to separate the suspended particles.展开更多
Aiming at the spatial pattern phenomenon in biochemical reactions,an enzyme-reaction Sporns-Seelig model with cross-diffusion is chosen as study object.Applying the central manifold theory,normal form method,local Hop...Aiming at the spatial pattern phenomenon in biochemical reactions,an enzyme-reaction Sporns-Seelig model with cross-diffusion is chosen as study object.Applying the central manifold theory,normal form method,local Hopf bifurcation theorem and perturbation theory,we study Turing instability of the spatially homogeneous Hopf bifurcation periodic solutions.At last,the theoretical results are verified by numerical simulations.展开更多
This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parametor nonlinear problem satisfying a Z2symnletry condition. Our aim is to present a new al,proach to ...This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parametor nonlinear problem satisfying a Z2symnletry condition. Our aim is to present a new al,proach to the theoretical and computational analysis of the bifurcating Hopf branches at this singular point by using the system designed to calculate Hopf points and exploring its symmetry. It is shown that a Hopf/Pitchfork point is a pitchfork bifurcation point in the system.Hence standard continuation and branch-switching can be used to compute these Hopf branches. In addition, an effect method based on the extended system of the singular points is developed for the computation of branch of secondary (nonsymmetric) Hopf points. The implementation of Newton's method for solving the extended system is also discussed. A numerical example is given.Keyworks: Hopf/Pitchfork point, Z2-symmetry, Hopf point, bifurcation, Extended system展开更多
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
According to the H_(∞)principle,the dynamical performance optimization of a quasi-zero-stiffness(QZS)isolation system with an additional tuned viscous inerter damper(TVID)is studied by using analytical method.The app...According to the H_(∞)principle,the dynamical performance optimization of a quasi-zero-stiffness(QZS)isolation system with an additional tuned viscous inerter damper(TVID)is studied by using analytical method.The approximate analytical solutions of the QZS system coupled with TVID are solved by using the complexification-averaging method,and the expression of stability conditions for steady-state solutions is derived based on Lyapunov method and Routh-Hurwitz criterion.Based on the fixed-point theory,considering the nonlinear stiffness and weak damping of the primary system,the stiffness and damping ratios of TVID coupled to QZS system are optimized by using the equal-peak method.The detailed analysis is conducted on the impact of TVID parameters and their corresponding optimization parameters on the dynamic behavior of the QZS primary system,including saddle-node(SN)bifurcation,Hopf bifurcation,backbone curve of amplitude-frequency response,and force transmissibility.According to the analysis,it is found that the steady-state motion of the system can enter quasi-periodic motion or even chaotic motion after losing stability through Hopf bifurcation.By optimizing the parameters of TVID,the number of SN bifurcation regions of the QZS main system can be reduced from 2 to 1,the Hopf bifurcation region can be eliminated,and the number of branches of backbone curve can be reduced from 2 to 1,thereby improving the dynamical performance of the QZS system.展开更多
We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection beco...We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection becomes unstable via a Hopf bifurcation at a critical temperature TC,giving rise to spontaneous periodic motion.Linear stability analysis yields analytical expressions for the critical oscillation temperature TC and the oscillation period at onset.Numerical simulations of the nonlinear equations confirm the bifurcation and reveal how key parameters(stiffness,thermal softening,thermal coupling,etc.)govern the oscillation amplitude and waveform.Finally,we demonstrate that the self-oscillating sheet can perform mechanical work as a heat engine,and we compare its performance to the Carnot efficiency limit.This work provides design principles for thermally driven selfoscillators with potential applications in soft robotics,adaptive structures,and thermal energy harvesting.展开更多
More than 30%of the earth's land surface is covered by the forest.Increase in population undergoes activities like construction,grazing,agriculture activities,and industrialization causing permanent clearing of la...More than 30%of the earth's land surface is covered by the forest.Increase in population undergoes activities like construction,grazing,agriculture activities,and industrialization causing permanent clearing of land to make room for something besides the forest,which is called deforestation.Considering this scenario,the mathematical model is framed for studying the dynamics with using four compartments such as deforestation of the dense forest,deforestation of the urban forest,population growth and wood industrialization.Using the dynamical phenomenon,the boundedness of the system is proposed.The proposed model has five equilibria.Behaviour of the system around all feasible equilibria is scrutinized through local stability theory of diferential equations.The 3d phase portrait gives the chaotic behavior of each compartment.Basic reproduction number value assists the bifurcation and the sensitivity analysis.Bifurcation analysis gives the ideal value,then the comparison of threshold and ideal value suggests the permissible situation of the compartment.For these findings,analytics results are verified through numerically validated data.展开更多
One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite...One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite equilibria exhibits complex bifurcation characteris-tics.The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed.An improved dynamic state feed-back control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled.A hybrid controller that includes both nonlinear and linear controllers is set up for the system.With the method,the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved.Numerical analysis verified the correctness.展开更多
This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density...This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density of prey species with interval parameters.The model develops with natural interval parameters since the uncertainties of parameters of any ecological system are a widespread phenomenon in nature.The equilibria of the model are obtained,and the dynamic behaviours of the proposed system are examined.Simulations of the model are performed for different parameters of the model.Numerical simulations show that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.Our study,through analytical derivation and numerical example,presents the effect of refuge on population dynamics under imprecise biological parameters.展开更多
This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging...This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging the two movable mirrors.We examine the chaotic dynamics under the influence of both single and bichromatic laser fields.The single laser field represents a system driven exclusively by the pump field,whereas the bichromatic field represents simultaneous driving by both the pump and probe fields.In addition to conventional chaos-inducing methods through parameter variations,we demonstrate that increasing the Coulomb coupling strength enhances the system’s nonlinearity and induces chaotic behavior.Furthermore,we propose several strategies for generating and controlling chaos,while also identifying the parameter ranges necessary for the resonance of the two mechanical oscillators.Interestingly,when adjusting the driving power in a system driven solely by the pump field,we unexpectedly observe the emergence of high-order sidebands.These findings contribute to the development of chaotic behavior in future cavity optomechanical systems and provide a theoretical basis for applications in physical random number generation and secure communication.展开更多
This paper studies a dual-channel green supply chain consisting of one manufacturer and one retailer in presence of government green subsidy and cap-and-trade regulation policies.We first develop and analyze a single-...This paper studies a dual-channel green supply chain consisting of one manufacturer and one retailer in presence of government green subsidy and cap-and-trade regulation policies.We first develop and analyze a single-period Stackelberg and a multi-period dynamic Stackelberg game models respectively with consistent pricing strategy.Subsequently,we extend these two game models by utilizing an inconsistent pricing strategy.The optimal solutions for the single-period Stackelberg game models in both scenarios are derived by means of the backward induction approach.Moreover,the existence and local asymptotic stability of the equilibrium points of the multi-period dynamic Stackelberg game models are examined,and the complex dynamics of chain members'long-term strategy evolution are investigated through chaos theory and numerical simulation.Additionally,the variable feedback control and time-delay feedback control method are utilized to eliminate system chaos respectively.The results indicate that(i)The excessive fast adjustment speeds by the manufacturer have a destabilizing effect on the stability of the Nash equilibrium point.(ii)The manufacturer's profits are improved with green subsidy degree increases,while its impact on the retailer's profits depends on certain parameter conditions,and the high carbon trading price is disadvantage to both chain members.(iii)The system's motion can transition from a steady state to a chaotic period through period-doubling or Neimark–Sacker bifurcations.(iv)The system's steady state is conducive to the manufacturer,while the retailer can benefit from the system's periodic cycles.Furthermore,both chain members'profits are declined when the system becomes chaotic.Lastly,the variable feedback and time-delay feedback control method can effectively eliminate system chaos.展开更多
This paper deeply introduces a brand-new research method for the synchronous characteristics of DC microgrid bus voltage and an improved synchronous control strategy.This method mainly targets the problem of bus volta...This paper deeply introduces a brand-new research method for the synchronous characteristics of DC microgrid bus voltage and an improved synchronous control strategy.This method mainly targets the problem of bus voltage oscillation caused by the bifurcation behavior of DC microgrid converters.Firstly,the article elaborately establishes a mathematical model of a single distributed power source with hierarchical control.On this basis,a smallworld network model that can better adapt to the topology structure of DC microgrids is further constructed.Then,a voltage synchronization analysis method based on the main stability function is proposed,and the synchronous characteristics of DC bus voltage are deeply studied by analyzing the size of the minimum non-zero eigenvalue.In view of the situation that the line coupling strength between distributed power sources is insufficient to achieve bus voltage synchronization,this paper innovatively proposes a new improved adaptive controller to effectively control voltage synchronization.And the convergence of the designed controller is strictly proved by using Lyapunov’s stability theorem.Finally,the effectiveness and feasibility of the designed controller in this paper are fully verified through detailed simulation experiments.After comparative analysis with the traditional adaptive controller,it is found that the newly designed controller can make the bus voltages of each distributed power source achieve synchronization more quickly,and is significantly superior to the traditional adaptive controller in terms of anti-interference performance.展开更多
0 INTRODUCTION Natural geomaterials,including soils and rocks,are invariably exposed to intricate stress conditions,in addition to water pressure,in various engineering contexts such as foundation treatment,mining,and...0 INTRODUCTION Natural geomaterials,including soils and rocks,are invariably exposed to intricate stress conditions,in addition to water pressure,in various engineering contexts such as foundation treatment,mining,and tunneling.These geomaterials frequently contain numerous fractures,which significantly influence hydrological dynamics as water permeates through them,leading to processes like expansion and bifurcation(Shu et al.,2023;Tran and Jha,2021;Lei et al.,2017;Wang et al.,2015).展开更多
This article is devoted to the study of the neural mechanisms of the binary substance of the brain in the process of creating,presenting and evaluating new approaches,methods and tools in the field of art.The interrel...This article is devoted to the study of the neural mechanisms of the binary substance of the brain in the process of creating,presenting and evaluating new approaches,methods and tools in the field of art.The interrelation and interdependence of genetically determined neural structures in the subcortical sphere and the neocortex in the creative process are shown.The scientific interpretation of the concepts of trance and bifurcation as mechanisms for the emergence of a new approach,method,and means for an innovator is given,and the peculiarities of perception and identification of innovations by art connoisseurs are characterized.展开更多
The increasingly stringent performance requirements of modern flight vehicles expose the possibilities of their coupled nonlinearities.Nevertheless,the aeroelastic response of a flight vehicle is generally predicted w...The increasingly stringent performance requirements of modern flight vehicles expose the possibilities of their coupled nonlinearities.Nevertheless,the aeroelastic response of a flight vehicle is generally predicted with isolated aerodynamic or structural nonlinearity.In this study,a Three-Degree-of-Freedom(3-DOF)aeroelastic model is proposed,which combines control surface hysteresis stiffness and dynamic stall aerodynamics.A control surface hysteretic model is applied to represent the nonlinear structural dynamics.The Office National d’Etudes et de Recherches Aérospatiales(ONERA)dynamic stall model is extended to a 3-DOF airfoil,considering the dynamic behavior of the control surface.The nonlinear aeroelastic model of a 3-DOF airfoil is described using a monolithic state-space equation.Henon’s event-driven scheme is used to investigate the post-flutter behavior of a 3-DOF airfoil with control surface hysteresis stiffness in a dynamic stall flow.The results indicate that the proposed model improves the numerical precision of nonlinear aerodynamic load by almost double that of the ONERA model that does not consider the dynamic behavior of the control surface.The flutter onset speed of the coupled nonlinear airfoil is overestimated by 10%using decoupled nonlinear analysis.Furthermore,the airfoil is dominated by the structural hysteresis nonlinearity and aerodynamic energy from the plunge motion at low airspeeds.As the airspeed increases,the airfoil is governed by the aerodynamic stall nonlinearity and aerodynamic energy from the pitch motion.The switch of the dominant nonlinearity induces topological changes in the aerodynamic curves,along with a threefold increase in the aerodynamic power.Excited by the increased energy,the airfoil undergoes a period-doubling bifurcation and transition to a higher-amplitude limit cycle.The theoretical results of this study are beneficial for the load design of modern flight vehicles under coupled nonlinear conditions.展开更多
The intricate relationship between origami and mechanism underscores the fertile ground for innovation,which is particularly evident in the construction theory of thick-panel origami.Despite its potential,thick panel ...The intricate relationship between origami and mechanism underscores the fertile ground for innovation,which is particularly evident in the construction theory of thick-panel origami.Despite its potential,thick panel origami remains relatively unexplored in the context of single-loop metamorphic mechanisms.Drawing inspiration from thickpanel origami,particularly Miura origami,this study proposes a pioneering single-loop 6R multiple metamorphic mechanism.Through rigorous mathematical modeling(including the construction and resolution of the D-H closed-loop equation)and leveraging advanced analytical tools such as the screw theory and Lie theory,this study meticulously elucidates the planar,spherical,and Bennett motion branches of the mechanism.Furthermore,it delineates all the three bifurcation points between the motion branches,thereby providing a comprehensive understanding of the kinematic behavior of the mechanism.A metamorphic network can be constructed by applying several single-loop mechanisms to a symmetrical layout.Owing to its metamorphic properties,this network can act as a structural backbone for deployable antennas,aerospace shelters,and morphing wing units,thereby enabling a single mechanism to achieve multiple folding configurations.This paper not only introduces innovative metamorphic mechanisms but also suggests a promising method for uncovering and designing metamorphic mechanisms by developing new mechanisms from thick-panel origami.展开更多
In a fractal zeta universe of bifurcated, ripped spacetime, the Millikan experiment, the quantum Hall effect, atmospheric clouds and universe clouds are shown to be self-similar with mass ratio of about 1020. Chaotic ...In a fractal zeta universe of bifurcated, ripped spacetime, the Millikan experiment, the quantum Hall effect, atmospheric clouds and universe clouds are shown to be self-similar with mass ratio of about 1020. Chaotic one-dimensional period-doublings as iterated hyperelliptic-elliptic curves are used to explain n-dim Kepler- and Coulomb singularities. The cosmic microwave background and cosmic rays are explained as bifurcated, ripped spacetime tensile forces. First iterated binary tree cloud cycles are related to emissions 1…1000 GHz. An interaction-independent universal vacuum density allows to predict large area correlated cosmic rays in quantum Hall experiments which would generate local nuclear disintegration stars, enhanced damage of layers and enhanced air ionization. A self-similarity between conductivity plateau and atmospheric clouds is extended to correlations in atmospheric layer, global temperature and climate.展开更多
基金Supported by the National Natural Science Foundation of China (10961017)"Qinglan" Talent Programof Lanzhou Jiaotong University (QL-05-20A)
文摘A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.
文摘We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species or prey, and a type III Holling functional response for the middle and highest trophic species (first and second predator respectively). We prove that this model exhibits two small amplitud periodic solutions bifurcating simultaneously each one from one of the two zero-Hopf equilibrium points that the model has adequate values of its parameters. As far as we know, this is the first time that the phenomena appear in the literature related with food chain models.
基金the National Natural Science Foundation of China and National Education Committee of China Science Foundation.
文摘The bifurcation of the second-order approximate solutions of nonlinear parametrically excited systems possessing generalized van der Pol's dampings and quintic Duffing's nonlinearities subjected to a primary parametric resonance is investigated. Using singularity theory with Z2-symmetry, bifurcations of the solutions are universally classified in a topologically equivalent sense for Z2-codimension>3. The question of whether the approximate solutions from the classical perturbation methods can be topologically equivalent in describing the periodic responses and the bifurcations of the original systems is made clear. The numerical results indicate that the vibration characteristic may suddenly disappear in the range of Z2-codimension>4.
文摘In this study the Zweifach-Fung effect is investigated in a Y-shaped bifurcation when the clearance between the rigid spherical particle and the walls is small compared to both channel’s and particle’s radii.Single-and two-particle systems are studied using resolved computational fluid dynamics coupled to discrete element method to obtain a two-dimensional map of the initially positioned particles that would enter each child branch.In all cases,the path selection of the sphere depends on its two-dimensional positioning far from the bifurcation region in the parent channel.Increasing the flow rate ratio or decreasing the Reynolds number intensifies the Zweifach-Fung bifurcation effect in a single-particle system.Similarly,in two-particle systems where non-contact particle-particle interaction is present,decreasing the particle-to-particle distance reduces the bifurcation effect,while changing the Reynolds number has the same influence as in the single-particle systems.The results provide insight for optimizing the flow characteristics in bifurcating microchannels to separate the suspended particles.
基金supported by Scientific Research and Innovation Fund for PhD Student:Research on the bifurcation problems of diffusive oncolytic virotherapy system(No.3072022CFJ2401).
文摘Aiming at the spatial pattern phenomenon in biochemical reactions,an enzyme-reaction Sporns-Seelig model with cross-diffusion is chosen as study object.Applying the central manifold theory,normal form method,local Hopf bifurcation theorem and perturbation theory,we study Turing instability of the spatially homogeneous Hopf bifurcation periodic solutions.At last,the theoretical results are verified by numerical simulations.
文摘This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parametor nonlinear problem satisfying a Z2symnletry condition. Our aim is to present a new al,proach to the theoretical and computational analysis of the bifurcating Hopf branches at this singular point by using the system designed to calculate Hopf points and exploring its symmetry. It is shown that a Hopf/Pitchfork point is a pitchfork bifurcation point in the system.Hence standard continuation and branch-switching can be used to compute these Hopf branches. In addition, an effect method based on the extended system of the singular points is developed for the computation of branch of secondary (nonsymmetric) Hopf points. The implementation of Newton's method for solving the extended system is also discussed. A numerical example is given.Keyworks: Hopf/Pitchfork point, Z2-symmetry, Hopf point, bifurcation, Extended system
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
基金supported by the National Natural Science Foundation of China(Grant Nos.12272241,12202286,and U1934201)Natural Science Foundation of Hebei Province(Grant Nos.A2021210012 and A2024210041).
文摘According to the H_(∞)principle,the dynamical performance optimization of a quasi-zero-stiffness(QZS)isolation system with an additional tuned viscous inerter damper(TVID)is studied by using analytical method.The approximate analytical solutions of the QZS system coupled with TVID are solved by using the complexification-averaging method,and the expression of stability conditions for steady-state solutions is derived based on Lyapunov method and Routh-Hurwitz criterion.Based on the fixed-point theory,considering the nonlinear stiffness and weak damping of the primary system,the stiffness and damping ratios of TVID coupled to QZS system are optimized by using the equal-peak method.The detailed analysis is conducted on the impact of TVID parameters and their corresponding optimization parameters on the dynamic behavior of the QZS primary system,including saddle-node(SN)bifurcation,Hopf bifurcation,backbone curve of amplitude-frequency response,and force transmissibility.According to the analysis,it is found that the steady-state motion of the system can enter quasi-periodic motion or even chaotic motion after losing stability through Hopf bifurcation.By optimizing the parameters of TVID,the number of SN bifurcation regions of the QZS main system can be reduced from 2 to 1,the Hopf bifurcation region can be eliminated,and the number of branches of backbone curve can be reduced from 2 to 1,thereby improving the dynamical performance of the QZS system.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2025B1515020077 and 2024A15150301-39)the National Natural Science Foundation of China(Grant No.12205138)the Shenzhen Science and Technology Innovation Committee(Grant No.JCYJ2022-0530113206015).
文摘We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection becomes unstable via a Hopf bifurcation at a critical temperature TC,giving rise to spontaneous periodic motion.Linear stability analysis yields analytical expressions for the critical oscillation temperature TC and the oscillation period at onset.Numerical simulations of the nonlinear equations confirm the bifurcation and reveal how key parameters(stiffness,thermal softening,thermal coupling,etc.)govern the oscillation amplitude and waveform.Finally,we demonstrate that the self-oscillating sheet can perform mechanical work as a heat engine,and we compare its performance to the Carnot efficiency limit.This work provides design principles for thermally driven selfoscillators with potential applications in soft robotics,adaptive structures,and thermal energy harvesting.
基金Supported by the DST-FIST file(#MSI-097)funded by UGC granted National Fellowship for Other Backward Classes(NFO-2018-19-OBC-GUJ-71790)funded by a Junior Research Fellowship from the Council of Scientific&Industrial Research(09/07(0061)/2019-EMR-I)。
文摘More than 30%of the earth's land surface is covered by the forest.Increase in population undergoes activities like construction,grazing,agriculture activities,and industrialization causing permanent clearing of land to make room for something besides the forest,which is called deforestation.Considering this scenario,the mathematical model is framed for studying the dynamics with using four compartments such as deforestation of the dense forest,deforestation of the urban forest,population growth and wood industrialization.Using the dynamical phenomenon,the boundedness of the system is proposed.The proposed model has five equilibria.Behaviour of the system around all feasible equilibria is scrutinized through local stability theory of diferential equations.The 3d phase portrait gives the chaotic behavior of each compartment.Basic reproduction number value assists the bifurcation and the sensitivity analysis.Bifurcation analysis gives the ideal value,then the comparison of threshold and ideal value suggests the permissible situation of the compartment.For these findings,analytics results are verified through numerically validated data.
基金Supported by the Guiding Project of Science and Technology Research Plan of Hubei Provincial Department of Education(B2022458)。
文摘One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite equilibria exhibits complex bifurcation characteris-tics.The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed.An improved dynamic state feed-back control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled.A hybrid controller that includes both nonlinear and linear controllers is set up for the system.With the method,the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved.Numerical analysis verified the correctness.
文摘This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density of prey species with interval parameters.The model develops with natural interval parameters since the uncertainties of parameters of any ecological system are a widespread phenomenon in nature.The equilibria of the model are obtained,and the dynamic behaviours of the proposed system are examined.Simulations of the model are performed for different parameters of the model.Numerical simulations show that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.Our study,through analytical derivation and numerical example,presents the effect of refuge on population dynamics under imprecise biological parameters.
基金supported by Young Talents from Longyuan,Gansu Province(Liwei Liu),the Fundamental Research Funds for the Central Universities,Northwest Minzu University(Grant No.31920230134)Teaching Achievement Cultivation Project of Gansu Province Department of Education(Grant No.2022GSJXCGPY-46)+1 种基金Special research topic on curriculum and teaching materials for primary,secondary and higher schools,Gansu Province Department of Education(Grant No.GSJC-Y2024204)Quality improvement project for undergraduate talent training,Northwest Minzu University(Grant Nos.2024YBJG-04 and 2024FCTD-03).
文摘This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging the two movable mirrors.We examine the chaotic dynamics under the influence of both single and bichromatic laser fields.The single laser field represents a system driven exclusively by the pump field,whereas the bichromatic field represents simultaneous driving by both the pump and probe fields.In addition to conventional chaos-inducing methods through parameter variations,we demonstrate that increasing the Coulomb coupling strength enhances the system’s nonlinearity and induces chaotic behavior.Furthermore,we propose several strategies for generating and controlling chaos,while also identifying the parameter ranges necessary for the resonance of the two mechanical oscillators.Interestingly,when adjusting the driving power in a system driven solely by the pump field,we unexpectedly observe the emergence of high-order sidebands.These findings contribute to the development of chaotic behavior in future cavity optomechanical systems and provide a theoretical basis for applications in physical random number generation and secure communication.
基金Project supported by the General Projects of Philosophy and Social Science Research in Jiangsu Province Universities(Grant No.2024SJYB1101)the National Youth Fund Guidance Project of Jiangsu University of Science and Technology(Zhangjiagang Campus)+2 种基金the Special Project for Cultivating Leading Talents in Philosophy and Social Science Planning of Zhejiang Province,China(Grant No.22YJRC14ZD)the Shanghai Pujiang Program(Grant No.2021PJC066)the National Natural Science Foundation of China(Grant No.72302142)。
文摘This paper studies a dual-channel green supply chain consisting of one manufacturer and one retailer in presence of government green subsidy and cap-and-trade regulation policies.We first develop and analyze a single-period Stackelberg and a multi-period dynamic Stackelberg game models respectively with consistent pricing strategy.Subsequently,we extend these two game models by utilizing an inconsistent pricing strategy.The optimal solutions for the single-period Stackelberg game models in both scenarios are derived by means of the backward induction approach.Moreover,the existence and local asymptotic stability of the equilibrium points of the multi-period dynamic Stackelberg game models are examined,and the complex dynamics of chain members'long-term strategy evolution are investigated through chaos theory and numerical simulation.Additionally,the variable feedback control and time-delay feedback control method are utilized to eliminate system chaos respectively.The results indicate that(i)The excessive fast adjustment speeds by the manufacturer have a destabilizing effect on the stability of the Nash equilibrium point.(ii)The manufacturer's profits are improved with green subsidy degree increases,while its impact on the retailer's profits depends on certain parameter conditions,and the high carbon trading price is disadvantage to both chain members.(iii)The system's motion can transition from a steady state to a chaotic period through period-doubling or Neimark–Sacker bifurcations.(iv)The system's steady state is conducive to the manufacturer,while the retailer can benefit from the system's periodic cycles.Furthermore,both chain members'profits are declined when the system becomes chaotic.Lastly,the variable feedback and time-delay feedback control method can effectively eliminate system chaos.
基金supported by the National Natural Science Foundation of China(Nos.51767017 and 51867015)the Basic Research and Innovation Group Project of Gansu(No.18JR3RA13)the Major Science and Technology Project of Gansu(No.19ZD2GA003).
文摘This paper deeply introduces a brand-new research method for the synchronous characteristics of DC microgrid bus voltage and an improved synchronous control strategy.This method mainly targets the problem of bus voltage oscillation caused by the bifurcation behavior of DC microgrid converters.Firstly,the article elaborately establishes a mathematical model of a single distributed power source with hierarchical control.On this basis,a smallworld network model that can better adapt to the topology structure of DC microgrids is further constructed.Then,a voltage synchronization analysis method based on the main stability function is proposed,and the synchronous characteristics of DC bus voltage are deeply studied by analyzing the size of the minimum non-zero eigenvalue.In view of the situation that the line coupling strength between distributed power sources is insufficient to achieve bus voltage synchronization,this paper innovatively proposes a new improved adaptive controller to effectively control voltage synchronization.And the convergence of the designed controller is strictly proved by using Lyapunov’s stability theorem.Finally,the effectiveness and feasibility of the designed controller in this paper are fully verified through detailed simulation experiments.After comparative analysis with the traditional adaptive controller,it is found that the newly designed controller can make the bus voltages of each distributed power source achieve synchronization more quickly,and is significantly superior to the traditional adaptive controller in terms of anti-interference performance.
基金supported by the National Key R&D Program of China(No.2023YFC3008401)the National Natural Science Foundation of China(No.42372307)。
文摘0 INTRODUCTION Natural geomaterials,including soils and rocks,are invariably exposed to intricate stress conditions,in addition to water pressure,in various engineering contexts such as foundation treatment,mining,and tunneling.These geomaterials frequently contain numerous fractures,which significantly influence hydrological dynamics as water permeates through them,leading to processes like expansion and bifurcation(Shu et al.,2023;Tran and Jha,2021;Lei et al.,2017;Wang et al.,2015).
文摘This article is devoted to the study of the neural mechanisms of the binary substance of the brain in the process of creating,presenting and evaluating new approaches,methods and tools in the field of art.The interrelation and interdependence of genetically determined neural structures in the subcortical sphere and the neocortex in the creative process are shown.The scientific interpretation of the concepts of trance and bifurcation as mechanisms for the emergence of a new approach,method,and means for an innovator is given,and the peculiarities of perception and identification of innovations by art connoisseurs are characterized.
文摘The increasingly stringent performance requirements of modern flight vehicles expose the possibilities of their coupled nonlinearities.Nevertheless,the aeroelastic response of a flight vehicle is generally predicted with isolated aerodynamic or structural nonlinearity.In this study,a Three-Degree-of-Freedom(3-DOF)aeroelastic model is proposed,which combines control surface hysteresis stiffness and dynamic stall aerodynamics.A control surface hysteretic model is applied to represent the nonlinear structural dynamics.The Office National d’Etudes et de Recherches Aérospatiales(ONERA)dynamic stall model is extended to a 3-DOF airfoil,considering the dynamic behavior of the control surface.The nonlinear aeroelastic model of a 3-DOF airfoil is described using a monolithic state-space equation.Henon’s event-driven scheme is used to investigate the post-flutter behavior of a 3-DOF airfoil with control surface hysteresis stiffness in a dynamic stall flow.The results indicate that the proposed model improves the numerical precision of nonlinear aerodynamic load by almost double that of the ONERA model that does not consider the dynamic behavior of the control surface.The flutter onset speed of the coupled nonlinear airfoil is overestimated by 10%using decoupled nonlinear analysis.Furthermore,the airfoil is dominated by the structural hysteresis nonlinearity and aerodynamic energy from the plunge motion at low airspeeds.As the airspeed increases,the airfoil is governed by the aerodynamic stall nonlinearity and aerodynamic energy from the pitch motion.The switch of the dominant nonlinearity induces topological changes in the aerodynamic curves,along with a threefold increase in the aerodynamic power.Excited by the increased energy,the airfoil undergoes a period-doubling bifurcation and transition to a higher-amplitude limit cycle.The theoretical results of this study are beneficial for the load design of modern flight vehicles under coupled nonlinear conditions.
基金Supported by National Natural Science Foundation of China(Grant Nos.52192634,52305015,52335003)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515011268)Science and Technology Innovation Committee of Shenzhen(Grant Nos.GXWD20231129102029003,KQTD20210811090146075).
文摘The intricate relationship between origami and mechanism underscores the fertile ground for innovation,which is particularly evident in the construction theory of thick-panel origami.Despite its potential,thick panel origami remains relatively unexplored in the context of single-loop metamorphic mechanisms.Drawing inspiration from thickpanel origami,particularly Miura origami,this study proposes a pioneering single-loop 6R multiple metamorphic mechanism.Through rigorous mathematical modeling(including the construction and resolution of the D-H closed-loop equation)and leveraging advanced analytical tools such as the screw theory and Lie theory,this study meticulously elucidates the planar,spherical,and Bennett motion branches of the mechanism.Furthermore,it delineates all the three bifurcation points between the motion branches,thereby providing a comprehensive understanding of the kinematic behavior of the mechanism.A metamorphic network can be constructed by applying several single-loop mechanisms to a symmetrical layout.Owing to its metamorphic properties,this network can act as a structural backbone for deployable antennas,aerospace shelters,and morphing wing units,thereby enabling a single mechanism to achieve multiple folding configurations.This paper not only introduces innovative metamorphic mechanisms but also suggests a promising method for uncovering and designing metamorphic mechanisms by developing new mechanisms from thick-panel origami.
文摘In a fractal zeta universe of bifurcated, ripped spacetime, the Millikan experiment, the quantum Hall effect, atmospheric clouds and universe clouds are shown to be self-similar with mass ratio of about 1020. Chaotic one-dimensional period-doublings as iterated hyperelliptic-elliptic curves are used to explain n-dim Kepler- and Coulomb singularities. The cosmic microwave background and cosmic rays are explained as bifurcated, ripped spacetime tensile forces. First iterated binary tree cloud cycles are related to emissions 1…1000 GHz. An interaction-independent universal vacuum density allows to predict large area correlated cosmic rays in quantum Hall experiments which would generate local nuclear disintegration stars, enhanced damage of layers and enhanced air ionization. A self-similarity between conductivity plateau and atmospheric clouds is extended to correlations in atmospheric layer, global temperature and climate.
