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
Hepatitis B Virus(HBV)infection and heavy alcohol consumption are the two primary pathogenic causes of liver cirrhosis.In this paper,we proposed a deterministic mathematical model and a logistic equation to investigat...Hepatitis B Virus(HBV)infection and heavy alcohol consumption are the two primary pathogenic causes of liver cirrhosis.In this paper,we proposed a deterministic mathematical model and a logistic equation to investigate the dynamics of liver cirrhosis progression as well as to explain the implications of variations in alcohol consumption on chronic hepatitis B patients,respectively.The intricate interactions between liver cirrhosis,recovery,and treatment dynamics are captured by the model.This study aims to show that alcohol consumption by Hepatitis B-infected individuals accelerates liver cirrhosis progression while treatment of acutely infected individuals reduces it.We proved that a unique solution of the proposed model exists,which is positive and bounded.Using the next-generation matrix approach,two basic reproductive numbers R_(A_(0))and R_(A_(max))are calculated to identify future recurrence.The equilibrium points are calculated,and both equilibria are proved locally and globally asymptotically stable when R_(0)is below and above one,respectively.It is shown that bifurcation exists at R_(0)=1 and a detailed proof for forward bifurcation is given.Furthermore,we performed the sensitivity analysis of the model parameters on R_(0).For the confirmation of analytical work,we performed numerical simulations,and the results indicate that the treatment and the inhibitory effects reduce the risk of developing liver cirrhosis in individuals,while heavy alcohol consumption accelerates markedly the liver cirrhosis progression in patients with chronic hepatitis B.展开更多
This study constructs a dual-capacitor neuron circuit(connected via a memristor)integrated with a phototube and a thermistor to simulate the ability of biological neurons to simultaneously perceive light and thermal s...This study constructs a dual-capacitor neuron circuit(connected via a memristor)integrated with a phototube and a thermistor to simulate the ability of biological neurons to simultaneously perceive light and thermal stimuli.The circuit model converts photothermal signals into electrical signals,and its dynamic behavior is described using dimensionless equations derived from Kirchhoff's laws.Based on Helmholtz's theorem,a pseudo-Hamiltonian energy function is introduced to characterize the system's energy metabolism.Furthermore,an adaptive control function is proposed to elucidate temperature-dependent firing mechanisms,in which temperature dynamics are regulated by pseudo-Hamiltonian energy.Numerical simulations using the fourth-order Runge-Kutta method,combined with bifurcation diagrams,Lyapunov exponent spectra,and phase portraits,reveal that parameters such as capacitance ratio,phototube voltage amplitude/frequency,temperature,and thermistor reference resistance significantly modulate neuronal firing patterns,inducing transitions between periodic and chaotic states.Periodic states typically exhibit higher average pseudo-Hamiltonian energy than chaotic states.Two-parameter analysis demonstrates that phototube voltage amplitude and temperature jointly govern firing modes,with chaotic behavior emerging within specific parameter ranges.Adaptive control studies show that gain/attenuation factors,energy thresholds,ceiling temperatures,and initial temperatures regulate the timing and magnitude of system temperature saturation.During both heating and cooling phases,temperature dynamics are tightly coupled with pseudoHamiltonian energy and neuronal firing activity.These findings validate the circuit's ability to simulate photothermal perception and adaptive temperature regulation,contributing to a deeper understanding of neuronal encoding mechanisms and multimodal sensory processing.展开更多
We incorporate a non-Markovian feedback mechanism into the simulated bifurcation method for dynamical solvers addressing combinatorial optimization problems.By reinjecting a portion of dissipated kinetic energy into e...We incorporate a non-Markovian feedback mechanism into the simulated bifurcation method for dynamical solvers addressing combinatorial optimization problems.By reinjecting a portion of dissipated kinetic energy into each spin in a history-dependent and trajectory-informed manner,the method effectively suppresses early freezing induced by inelastic boundaries and enhances the system's ability to explore complex energy landscapes.Numerical results on the maximum cut(MAX-CUT)instances of fully connected Sherrington–Kirkpatrick(SK)spin glass models,including the 2000-spin K_(2000)benchmark,demonstrate that the non-Markovian algorithm significantly improves both solution quality and convergence speed.Tests on randomly generated SK instances with 100 to 1000 spins further indicate favorable scalability and substantial gains in computational efficiency.Moreover,the proposed scheme is well suited for massively parallel hardware implementations,such as field-programmable gate arrays,providing a practical and scalable approach for solving large-scale combinatorial optimization problems.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
Model-free,data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science.Stimulated by the recent progress in machine learning,considerable attention has been given to the inference of ch...Model-free,data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science.Stimulated by the recent progress in machine learning,considerable attention has been given to the inference of chaos by the technique of reservoir computing(RC).In particular,by incorporating a parameter-control channel into the standard RC,it is demonstrated that the machine is able to not only replicate the dynamics of the training states,but also infer new dynamics not included in the training set.The new machine-learning scheme,termed parameter-aware RC,opens up new avenues for data-based analysis of chaotic systems,and holds promise for predicting and controlling many real-world complex systems.Here,using typical chaotic systems as examples,we give a comprehensive introduction to this powerful machine-learning technique,including the algorithm,the implementation,the performance,and the open questions calling for further studies.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
The SOS/ERK cascades are key signaling pathways that regulate cellular processes ranging from cellular proliferation,differentiation and apoptosis to tumor formation.However,the properties of these signaling pathways ...The SOS/ERK cascades are key signaling pathways that regulate cellular processes ranging from cellular proliferation,differentiation and apoptosis to tumor formation.However,the properties of these signaling pathways are not well understood.More importantly,how stochastic perturbations of internal and external cellular environment affect these pathways remains unanswered.To answer these questions,we,in this paper,propose a stochastic model according to the biochemical reaction processes of the SOS/ERK pathways,and,respectively,research the dynamical behaviors of this model under the four kinds of noises:Gaussian noise,colored noise,Lévy noise and fraction Brown noise.Some important results are found that Gaussian and colored noises have less effect on the stability of the system when the strength of the noise is small;Lévy and fractional Brownian noises significantly change the trajectories of the system.Power spectrum analysis shows that Lévy noise induces a system with quasi-periodic trajectories.Our results not only provide an understanding of the SOS/ERK pathway,but also show generalized rules for stochastic dynamical systems.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 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
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.
文摘Hepatitis B Virus(HBV)infection and heavy alcohol consumption are the two primary pathogenic causes of liver cirrhosis.In this paper,we proposed a deterministic mathematical model and a logistic equation to investigate the dynamics of liver cirrhosis progression as well as to explain the implications of variations in alcohol consumption on chronic hepatitis B patients,respectively.The intricate interactions between liver cirrhosis,recovery,and treatment dynamics are captured by the model.This study aims to show that alcohol consumption by Hepatitis B-infected individuals accelerates liver cirrhosis progression while treatment of acutely infected individuals reduces it.We proved that a unique solution of the proposed model exists,which is positive and bounded.Using the next-generation matrix approach,two basic reproductive numbers R_(A_(0))and R_(A_(max))are calculated to identify future recurrence.The equilibrium points are calculated,and both equilibria are proved locally and globally asymptotically stable when R_(0)is below and above one,respectively.It is shown that bifurcation exists at R_(0)=1 and a detailed proof for forward bifurcation is given.Furthermore,we performed the sensitivity analysis of the model parameters on R_(0).For the confirmation of analytical work,we performed numerical simulations,and the results indicate that the treatment and the inhibitory effects reduce the risk of developing liver cirrhosis in individuals,while heavy alcohol consumption accelerates markedly the liver cirrhosis progression in patients with chronic hepatitis B.
基金supported by the Natural Science Founda tion of Chongqing(Grant No.CSTB2024NSCQ-MSX0944)。
文摘This study constructs a dual-capacitor neuron circuit(connected via a memristor)integrated with a phototube and a thermistor to simulate the ability of biological neurons to simultaneously perceive light and thermal stimuli.The circuit model converts photothermal signals into electrical signals,and its dynamic behavior is described using dimensionless equations derived from Kirchhoff's laws.Based on Helmholtz's theorem,a pseudo-Hamiltonian energy function is introduced to characterize the system's energy metabolism.Furthermore,an adaptive control function is proposed to elucidate temperature-dependent firing mechanisms,in which temperature dynamics are regulated by pseudo-Hamiltonian energy.Numerical simulations using the fourth-order Runge-Kutta method,combined with bifurcation diagrams,Lyapunov exponent spectra,and phase portraits,reveal that parameters such as capacitance ratio,phototube voltage amplitude/frequency,temperature,and thermistor reference resistance significantly modulate neuronal firing patterns,inducing transitions between periodic and chaotic states.Periodic states typically exhibit higher average pseudo-Hamiltonian energy than chaotic states.Two-parameter analysis demonstrates that phototube voltage amplitude and temperature jointly govern firing modes,with chaotic behavior emerging within specific parameter ranges.Adaptive control studies show that gain/attenuation factors,energy thresholds,ceiling temperatures,and initial temperatures regulate the timing and magnitude of system temperature saturation.During both heating and cooling phases,temperature dynamics are tightly coupled with pseudoHamiltonian energy and neuronal firing activity.These findings validate the circuit's ability to simulate photothermal perception and adaptive temperature regulation,contributing to a deeper understanding of neuronal encoding mechanisms and multimodal sensory processing.
基金supported by the National Key Research and Development Program of China(Grant No.2024YFA1408500)the National Natural Science Foundation of China(Grant Nos.12174028 and 12574115)the Open Fund of the State Key Laboratory of Spintronics Devices and Technologies(Grant No.SPL-2408)。
文摘We incorporate a non-Markovian feedback mechanism into the simulated bifurcation method for dynamical solvers addressing combinatorial optimization problems.By reinjecting a portion of dissipated kinetic energy into each spin in a history-dependent and trajectory-informed manner,the method effectively suppresses early freezing induced by inelastic boundaries and enhances the system's ability to explore complex energy landscapes.Numerical results on the maximum cut(MAX-CUT)instances of fully connected Sherrington–Kirkpatrick(SK)spin glass models,including the 2000-spin K_(2000)benchmark,demonstrate that the non-Markovian algorithm significantly improves both solution quality and convergence speed.Tests on randomly generated SK instances with 100 to 1000 spins further indicate favorable scalability and substantial gains in computational efficiency.Moreover,the proposed scheme is well suited for massively parallel hardware implementations,such as field-programmable gate arrays,providing a practical and scalable approach for solving large-scale combinatorial optimization problems.
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Project supported by the National Natural Science Foundation of China(Grant No.12275165)XGW was also supported by the Fundamental Research Funds for the Central Universities(Grant No.GK202202003).
文摘Model-free,data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science.Stimulated by the recent progress in machine learning,considerable attention has been given to the inference of chaos by the technique of reservoir computing(RC).In particular,by incorporating a parameter-control channel into the standard RC,it is demonstrated that the machine is able to not only replicate the dynamics of the training states,but also infer new dynamics not included in the training set.The new machine-learning scheme,termed parameter-aware RC,opens up new avenues for data-based analysis of chaotic systems,and holds promise for predicting and controlling many real-world complex systems.Here,using typical chaotic systems as examples,we give a comprehensive introduction to this powerful machine-learning technique,including the algorithm,the implementation,the performance,and the open questions calling for further studies.
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 62066026,12071408,and 62363027 from NSF of Chinagrants PhD program of Entrepreneurship and Innovation of Jiangsu province,Jiangsu University"Blue Project"20224BAB202026 from NSF of Jiangxi province.
文摘The SOS/ERK cascades are key signaling pathways that regulate cellular processes ranging from cellular proliferation,differentiation and apoptosis to tumor formation.However,the properties of these signaling pathways are not well understood.More importantly,how stochastic perturbations of internal and external cellular environment affect these pathways remains unanswered.To answer these questions,we,in this paper,propose a stochastic model according to the biochemical reaction processes of the SOS/ERK pathways,and,respectively,research the dynamical behaviors of this model under the four kinds of noises:Gaussian noise,colored noise,Lévy noise and fraction Brown noise.Some important results are found that Gaussian and colored noises have less effect on the stability of the system when the strength of the noise is small;Lévy and fractional Brownian noises significantly change the trajectories of the system.Power spectrum analysis shows that Lévy noise induces a system with quasi-periodic trajectories.Our results not only provide an understanding of the SOS/ERK pathway,but also show generalized rules for stochastic dynamical systems.
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.
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.
