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
The nonlinear Schrodinger equation(NLSE) is a key tool for modeling wave propagation in nonlinear and dispersive media. This study focuses on the complex cubic NLSE with δ-potential,explored through the Brownian proc...The nonlinear Schrodinger equation(NLSE) is a key tool for modeling wave propagation in nonlinear and dispersive media. This study focuses on the complex cubic NLSE with δ-potential,explored through the Brownian process. The investigation begins with the derivation of stochastic solitary wave solutions using the modified exp(-Ψ(ξ)) expansion method. To illustrate the noise effects, 3D and 2D visualizations are displayed for different non-negative values of noise parameter under suitable parameter values. Additionally, qualitative analysis of both perturbed and unperturbed dynamical systems is conducted using bifurcation and chaos theory. In bifurcation analysis, we analyze the detailed parameter analysis near fixed points of the unperturbed system. An external periodic force is applied to perturb the system, leading to an investigation of its chaotic behavior. Chaos detection tools are employed to predict the behavior of the perturbed dynamical system, with results validated through visual representations.Multistability analysis is conducted under varying initial conditions to identify multiple stable states in the perturbed dynamical system, contributing to chaotic behavior. Also, sensitivity analysis of the Hamiltonian system is performed for different initial conditions. The novelty of this work lies in the significance of the obtained results, which have not been previously explored for the considered equation. These findings offer noteworthy insights into the behavior of the complex cubic NLSE with δ-potential and its applications in fields such as nonlinear optics, quantum mechanics and Bose–Einstein condensates.展开更多
The law of vehicle movement has long been studied under the umbrella of microscopic traffic flow models,especially the car-following(CF)models.These models of the movement of vehicles serve as the backbone of traffic ...The law of vehicle movement has long been studied under the umbrella of microscopic traffic flow models,especially the car-following(CF)models.These models of the movement of vehicles serve as the backbone of traffic flow analysis,simulation,autonomous vehicle development,etc.Two-dimensional(2D)vehicular movement is basically stochastic and is the result of interactions between a driver's behavior and a vehicle's characteristics.Current microscopic models either neglect 2D noise,or overlook vehicle dynamics.The modeling capabilities,thus,are limited,so that stochastic lateral movement cannot be reproduced.The present research extends an intelligent driver model(IDM)by explicitly considering both vehicle dynamics and 2D noises to formulate a stochastic 2D IDM model,with vehicle dynamics based on the stochastic differential equation(SDE)theory.Control inputs from the vehicle include the steer rate and longitudinal acceleration,both of which are developed based on an idea from a traditional intelligent driver model.The stochastic stability condition is analyzed on the basis of Lyapunov theory.Numerical analysis is used to assess the two cases:(i)when a vehicle accelerates from a standstill and(ii)when a platoon of vehicles follow a leader with a stop-and-go speed profile,the formation of congestion and subsequent dispersion are simulated.The results show that the model can reproduce the stochastic 2D trajectories of the vehicle and the marginal distribution of lateral movement.The proposed model can be used in both a simulation platform and a behavioral analysis of a human driver in traffic flow.展开更多
This paper addresses a dynamic vehicle routing problem with stochastic requests in a dual-channel distribution center that utilizes shared vehicle resources to serve two types of customers:offline corporate clients(CC...This paper addresses a dynamic vehicle routing problem with stochastic requests in a dual-channel distribution center that utilizes shared vehicle resources to serve two types of customers:offline corporate clients(CCs)with fixed and stochastic batch demands,and online individual customers(ICs)with single-unit demands.To manage stochastic batch demands from CCs,this paper proposes three recourse policies under a differentiated resource-sharing scheme:the waiting-tour-based(WTB)policy,the advance-tour-based(ATB)policy,and the advance-customer-based(ACB)policy.These policies differ in their response priorities to random requests and the scope of route reoptimization.The problem is formulated as a two-stage stochastic recourse programming model,where the first stage establishes routes for fixed demands.In the second stage,we construct three stochastic recourse programming models corresponding to the proposed recourse policies.To solve these models,this paper develop rolling horizon algorithms integrated with mathematical programming models or metaheuristic algorithms.Extensive numerical experiments validate the effectiveness of the proposed algorithms and policies.The results indicate that both the ATB and ACB policies lead to cost savings compared to the WTB policy,especially when stochastic demands are urgent and delivery resources are quite limited.Specifically,when the number of ICs is small,the expected total cost savings can exceed 12%,and in some scenarios,savings of over 20%can be achieved.When the number of ICs is large,some scenarios can achieve cost savings exceeding 7%.Furthermore,the ACB policy yields lower costs,fewer worsened ICs,fewer trips,and less vehicle time than the ATB policy.展开更多
The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics...The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach： One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.展开更多
This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequal...This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.展开更多
We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given s...We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar6 map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar6＇s cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincare＇s global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.展开更多
A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transforma...A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.展开更多
Dear Editor,This letter addresses the synchronization problem of a class of delayed stochastic complex dynamical networks consisting of multiple drive and response nodes.The aim is to achieve mean square exponential s...Dear Editor,This letter addresses the synchronization problem of a class of delayed stochastic complex dynamical networks consisting of multiple drive and response nodes.The aim is to achieve mean square exponential synchronization for the drive-response nodes despite the simultaneous presence of time delays and stochastic noises in node dynamics.展开更多
Sparsity of a parameter vector in stochastic dynamic systems and precise reconstruction of its zero and nonzero elements appear in many areas including systems and control[1-4],signal processing[5,6],statistics[7,8],a...Sparsity of a parameter vector in stochastic dynamic systems and precise reconstruction of its zero and nonzero elements appear in many areas including systems and control[1-4],signal processing[5,6],statistics[7,8],and machine learning[9,10]since it provides a way to discover a parsimonious model that leads to more reliable and robust prediction.Classical system identification theory has been a well-developed field[11,12].It usually characterizes the identification error between the estimates and the unknown parameters using different criteria such as randomness of noises,frequency domain sample data。展开更多
The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified resp...The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.展开更多
The mass flow rate of a granular flow through an aperture under gravity is a long-standing challenge issue in physical science. We show that for steady flow field close to laminar flow, the dynamical equations togethe...The mass flow rate of a granular flow through an aperture under gravity is a long-standing challenge issue in physical science. We show that for steady flow field close to laminar flow, the dynamical equations together with the continue equation and Mohr-circle description of the stress are closed, and hence solvable. In a case of streamline guided by the two-dimensional hopper, we obtain a consistent condition and use it to determine the stress and the velocity distribution. Our result indicates that 3/2 power scaling behavior is recovered with a coefficient C(μ,α) being a function of frictional coefficient and the hopper angle. It is found that the predicted coefficient C(μ,α) is compatible with previous studies.展开更多
We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for m...We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.展开更多
In this paper, an impulsive control strategy is proposed for a class of nonlinear stochastic dynamical networks with time-varying delay. Using the Lyapunov stability theory, a sufficient verifiable criterion for the e...In this paper, an impulsive control strategy is proposed for a class of nonlinear stochastic dynamical networks with time-varying delay. Using the Lyapunov stability theory, a sufficient verifiable criterion for the exponential synchronization is derived analytically. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed approach.展开更多
We consider the two-dimensional stochastic quasi-geostrophic equation ■=1/(R_e)△~2■-r/2△■+f(x,y,t)(1.1) on a regular bounded open domain D ■,where ■ is the stream function,F Froude Number (F≈O(1)),R_e Reynolds...We consider the two-dimensional stochastic quasi-geostrophic equation ■=1/(R_e)△~2■-r/2△■+f(x,y,t)(1.1) on a regular bounded open domain D ■,where ■ is the stream function,F Froude Number (F≈O(1)),R_e Reynolds number(R_e■10~2),β_0 a positive constant(β_0≈O(10^(-1)),r the Ekman dissipation constant(r≈o(1)),the external forcing term f(x,y,t)=-(dW)/(dt)(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the展开更多
The static comer frequency and dynamic comer frequency in stochastic synthesis of ground motion from fi- nite-fault modeling are introduced, and conceptual disadvantages of the two are discussed in this paper. Further...The static comer frequency and dynamic comer frequency in stochastic synthesis of ground motion from fi- nite-fault modeling are introduced, and conceptual disadvantages of the two are discussed in this paper. Furthermore, the non-uniform radiation of seismic wave on the fault plane, as well as the trend of the larger rupture area, the lower comer frequency, can be described by the source spectral model developed by the authors. A new dynamic comer frequency can be developed directly from the model. The dependence of ground motion on the size of subfault can be eliminated if this source spectral model is adopted in the synthesis. Finally, the approach presented is validated from the comparison between the synthesized and observed ground motions at six rock stations during the Northridge earthquake in 1994.展开更多
With dynamic reliability problems of stochastic parameters,supercavity vehicle is subject to impact loads.The supercavity vehicle is modeled by using eight-node super-parametric shell elements.The tail impact loads of...With dynamic reliability problems of stochastic parameters,supercavity vehicle is subject to impact loads.The supercavity vehicle is modeled by using eight-node super-parametric shell elements.The tail impact loads of supercavity vehicle structures are simplified into two stationary random processes with a certain phase difference,and the random excitations are transformed into sinusoidal ones in terms of the pseudo excitation method.The stress response of stochastic structure can be obtained through combining Newmark method with pseudo excitation perturbation method,and then all required digital features for dynamic reliability of supercavity vehicle have be calculated.The expressions of the mean value and the variance of dynamic reliability of supercavity vehicle with stochastic parameters are educed on the basis of the Poisson formula of calculating dynamic reliability.Finally,the influence of the randomness of structural parameters on the dynamic reliability is analyzed.And the feasibility and availability of this method were validated by comparing with the Monte Carlo method.展开更多
A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriat...A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.展开更多
A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented....A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices axe constructed based on the fuzzy factor method and random factor method; from the Rayleigh＇s quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic; the fuzzy numeric characteristics of dynamic characteristic axe then derived by using the random variable＇s moment function method and algebra synthesis method. Two examples axe used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.展开更多
This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process mode...This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process model, the imprecise probabilistic model rather than a precise probability distribution function is employed to characterize the uncertainty at each time point for a time-variant parameter, which provides an effective tool for problems with limited experimental samples. The linear correlation between variables at different time points for imprecise stochastic processes is described by defining the auto-correlation coefficient function and the crosscorrelation coefficient function. For the convenience of analysis, this paper gives the definition of the P-box-based imprecise stochastic process and categorizes it into two classes: parameterized and non-parameterized P-box-based imprecise stochastic processes. Besides, a time-variant reliability analysis approach is developed based on the P-box-based imprecise stochastic process model,through which the interval of dynamic reliability for a structure under uncertain dynamic excitations or time-variant factors can be obtained. Finally, the effectiveness of the proposed method is verified by investigating three numerical examples.展开更多
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Supporting Project under Grant No.RSP2025R472,King Saud University,Riyadh,Saudi Arabia。
文摘The nonlinear Schrodinger equation(NLSE) is a key tool for modeling wave propagation in nonlinear and dispersive media. This study focuses on the complex cubic NLSE with δ-potential,explored through the Brownian process. The investigation begins with the derivation of stochastic solitary wave solutions using the modified exp(-Ψ(ξ)) expansion method. To illustrate the noise effects, 3D and 2D visualizations are displayed for different non-negative values of noise parameter under suitable parameter values. Additionally, qualitative analysis of both perturbed and unperturbed dynamical systems is conducted using bifurcation and chaos theory. In bifurcation analysis, we analyze the detailed parameter analysis near fixed points of the unperturbed system. An external periodic force is applied to perturb the system, leading to an investigation of its chaotic behavior. Chaos detection tools are employed to predict the behavior of the perturbed dynamical system, with results validated through visual representations.Multistability analysis is conducted under varying initial conditions to identify multiple stable states in the perturbed dynamical system, contributing to chaotic behavior. Also, sensitivity analysis of the Hamiltonian system is performed for different initial conditions. The novelty of this work lies in the significance of the obtained results, which have not been previously explored for the considered equation. These findings offer noteworthy insights into the behavior of the complex cubic NLSE with δ-potential and its applications in fields such as nonlinear optics, quantum mechanics and Bose–Einstein condensates.
基金Project supported by the National Key Research and Development Program of China(Grant No.2021YFE0194400)the National Natural Science Foundation of China(Grant Nos.52272314 and 52131202)+1 种基金the Fund for Humanities and Social Science from the Ministry of Education of China(Grant No.21YJCZH116)the Public Welfare Scientific Research Project(Grant No.LGF22E080007)。
文摘The law of vehicle movement has long been studied under the umbrella of microscopic traffic flow models,especially the car-following(CF)models.These models of the movement of vehicles serve as the backbone of traffic flow analysis,simulation,autonomous vehicle development,etc.Two-dimensional(2D)vehicular movement is basically stochastic and is the result of interactions between a driver's behavior and a vehicle's characteristics.Current microscopic models either neglect 2D noise,or overlook vehicle dynamics.The modeling capabilities,thus,are limited,so that stochastic lateral movement cannot be reproduced.The present research extends an intelligent driver model(IDM)by explicitly considering both vehicle dynamics and 2D noises to formulate a stochastic 2D IDM model,with vehicle dynamics based on the stochastic differential equation(SDE)theory.Control inputs from the vehicle include the steer rate and longitudinal acceleration,both of which are developed based on an idea from a traditional intelligent driver model.The stochastic stability condition is analyzed on the basis of Lyapunov theory.Numerical analysis is used to assess the two cases:(i)when a vehicle accelerates from a standstill and(ii)when a platoon of vehicles follow a leader with a stop-and-go speed profile,the formation of congestion and subsequent dispersion are simulated.The results show that the model can reproduce the stochastic 2D trajectories of the vehicle and the marginal distribution of lateral movement.The proposed model can be used in both a simulation platform and a behavioral analysis of a human driver in traffic flow.
基金supported by the National Natural Science Foundation of China(71991464/71991460,72301261,72001066)2024 Anhui Province High-end Talent Introduction and Cultivation Project.
文摘This paper addresses a dynamic vehicle routing problem with stochastic requests in a dual-channel distribution center that utilizes shared vehicle resources to serve two types of customers:offline corporate clients(CCs)with fixed and stochastic batch demands,and online individual customers(ICs)with single-unit demands.To manage stochastic batch demands from CCs,this paper proposes three recourse policies under a differentiated resource-sharing scheme:the waiting-tour-based(WTB)policy,the advance-tour-based(ATB)policy,and the advance-customer-based(ACB)policy.These policies differ in their response priorities to random requests and the scope of route reoptimization.The problem is formulated as a two-stage stochastic recourse programming model,where the first stage establishes routes for fixed demands.In the second stage,we construct three stochastic recourse programming models corresponding to the proposed recourse policies.To solve these models,this paper develop rolling horizon algorithms integrated with mathematical programming models or metaheuristic algorithms.Extensive numerical experiments validate the effectiveness of the proposed algorithms and policies.The results indicate that both the ATB and ACB policies lead to cost savings compared to the WTB policy,especially when stochastic demands are urgent and delivery resources are quite limited.Specifically,when the number of ICs is small,the expected total cost savings can exceed 12%,and in some scenarios,savings of over 20%can be achieved.When the number of ICs is large,some scenarios can achieve cost savings exceeding 7%.Furthermore,the ACB policy yields lower costs,fewer worsened ICs,fewer trips,and less vehicle time than the ATB policy.
基金The project supported in part by USA NIH Grant under HG002894
文摘The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach： One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.
基金supported by the National Natural Science Foundation of China (Grant No.60974139)the Fundamental Research Funds for the Central Universities (Grant No.72103676)
文摘This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.
基金supported by the National Natural Science Foundation of China (11172260 and 11072213)the Fundamental Research Fund for the Central University of China (2011QNA4001)
文摘We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar6 map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar6＇s cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincare＇s global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.
基金supported in part by the National Natural Science Foundation of China(11771001)the Key Natural Science Research Project of Universities of Anhui Province,China(2022AH050108)。
文摘Dear Editor,This letter addresses the synchronization problem of a class of delayed stochastic complex dynamical networks consisting of multiple drive and response nodes.The aim is to achieve mean square exponential synchronization for the drive-response nodes despite the simultaneous presence of time delays and stochastic noises in node dynamics.
文摘Sparsity of a parameter vector in stochastic dynamic systems and precise reconstruction of its zero and nonzero elements appear in many areas including systems and control[1-4],signal processing[5,6],statistics[7,8],and machine learning[9,10]since it provides a way to discover a parsimonious model that leads to more reliable and robust prediction.Classical system identification theory has been a well-developed field[11,12].It usually characterizes the identification error between the estimates and the unknown parameters using different criteria such as randomness of noises,frequency domain sample data。
基金Project supported by the National Natural Science Foundation of China (Grant No.11002061)
文摘The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.
基金Supported by the Key Research Program of Frontier Science of the Chinese Academy of Sciences under Grant No QYZDYSSW-SYS006
文摘The mass flow rate of a granular flow through an aperture under gravity is a long-standing challenge issue in physical science. We show that for steady flow field close to laminar flow, the dynamical equations together with the continue equation and Mohr-circle description of the stress are closed, and hence solvable. In a case of streamline guided by the two-dimensional hopper, we obtain a consistent condition and use it to determine the stress and the velocity distribution. Our result indicates that 3/2 power scaling behavior is recovered with a coefficient C(μ,α) being a function of frictional coefficient and the hopper angle. It is found that the predicted coefficient C(μ,α) is compatible with previous studies.
基金Project supported by the Natural Science Foundation of Jiangsu Province (Grant No.BK20220917)the National Natural Science Foundation of China (Grant Nos.12001213 and 12302035)。
文摘We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.
文摘In this paper, an impulsive control strategy is proposed for a class of nonlinear stochastic dynamical networks with time-varying delay. Using the Lyapunov stability theory, a sufficient verifiable criterion for the exponential synchronization is derived analytically. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed approach.
基金Foundation item:The work was supported in part by the NSFC(No.90511009).
文摘We consider the two-dimensional stochastic quasi-geostrophic equation ■=1/(R_e)△~2■-r/2△■+f(x,y,t)(1.1) on a regular bounded open domain D ■,where ■ is the stream function,F Froude Number (F≈O(1)),R_e Reynolds number(R_e■10~2),β_0 a positive constant(β_0≈O(10^(-1)),r the Ekman dissipation constant(r≈o(1)),the external forcing term f(x,y,t)=-(dW)/(dt)(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the
基金supported by National Natural Science Foundation of China under grant No. 50778058 and 90715038National Key Technology Research and Development Program under grant No. 2006BAC13B02
文摘The static comer frequency and dynamic comer frequency in stochastic synthesis of ground motion from fi- nite-fault modeling are introduced, and conceptual disadvantages of the two are discussed in this paper. Furthermore, the non-uniform radiation of seismic wave on the fault plane, as well as the trend of the larger rupture area, the lower comer frequency, can be described by the source spectral model developed by the authors. A new dynamic comer frequency can be developed directly from the model. The dependence of ground motion on the size of subfault can be eliminated if this source spectral model is adopted in the synthesis. Finally, the approach presented is validated from the comparison between the synthesized and observed ground motions at six rock stations during the Northridge earthquake in 1994.
文摘With dynamic reliability problems of stochastic parameters,supercavity vehicle is subject to impact loads.The supercavity vehicle is modeled by using eight-node super-parametric shell elements.The tail impact loads of supercavity vehicle structures are simplified into two stationary random processes with a certain phase difference,and the random excitations are transformed into sinusoidal ones in terms of the pseudo excitation method.The stress response of stochastic structure can be obtained through combining Newmark method with pseudo excitation perturbation method,and then all required digital features for dynamic reliability of supercavity vehicle have be calculated.The expressions of the mean value and the variance of dynamic reliability of supercavity vehicle with stochastic parameters are educed on the basis of the Poisson formula of calculating dynamic reliability.Finally,the influence of the randomness of structural parameters on the dynamic reliability is analyzed.And the feasibility and availability of this method were validated by comparing with the Monte Carlo method.
基金supported by NSF of China (10901065, 10971225, and11028102)the NSF Grants 1025422 and 0731201the Cheung Kong Scholars Program, and an open research grant from the State Key Laboratory for Nonlinear Mechanics at the Chinese Academy of Sciences
文摘A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.
基金Project supported by the Natural Science Foundation of Shaanxi Province of China (No,A200214)
文摘A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices axe constructed based on the fuzzy factor method and random factor method; from the Rayleigh＇s quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic; the fuzzy numeric characteristics of dynamic characteristic axe then derived by using the random variable＇s moment function method and algebra synthesis method. Two examples axe used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.
基金supported by the Science Challenge Project,China(No.TZ2018007)the National Science Fund for Distinguished Young Scholars,China(No.51725502)+2 种基金the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(No.51621004)the Fundamental Research Foundation of China(No.JCKY2020110C105)the National Natural Science Foundation of China(No.52105253)。
文摘This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process model, the imprecise probabilistic model rather than a precise probability distribution function is employed to characterize the uncertainty at each time point for a time-variant parameter, which provides an effective tool for problems with limited experimental samples. The linear correlation between variables at different time points for imprecise stochastic processes is described by defining the auto-correlation coefficient function and the crosscorrelation coefficient function. For the convenience of analysis, this paper gives the definition of the P-box-based imprecise stochastic process and categorizes it into two classes: parameterized and non-parameterized P-box-based imprecise stochastic processes. Besides, a time-variant reliability analysis approach is developed based on the P-box-based imprecise stochastic process model,through which the interval of dynamic reliability for a structure under uncertain dynamic excitations or time-variant factors can be obtained. Finally, the effectiveness of the proposed method is verified by investigating three numerical examples.
