The asymptotic stability of a discrete logistic model with random growth coefficient is studied in this paper. Firstly, the discrete logistic model with random growth coefficient is built and reduced into its determin...The asymptotic stability of a discrete logistic model with random growth coefficient is studied in this paper. Firstly, the discrete logistic model with random growth coefficient is built and reduced into its deterministic equivalent system by orthogonal polynomial approximation. Then, the linear stability theory and the Jury criterion of nonlinear deterministic discrete systems are applied to the equivalent one. At last, by mathematical analysis, we find that the parameter interval for asymptotic stability of nontrivial equilibrium in stochastic logistic system gets smaller as the random intensity or statistical parameters of random variable is increased and the random parameter’s influence on asymptotic stability in stochastic logistic system becomes prominent.展开更多
The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system ...The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system by orthogonal polynomial approximation. Then, the linear stability theory and Routh-Hurwitz criterion for nonlinear deterministic systems are applied to the equivalent one. At last, at the aid of Lyapunov second method, we obtain that as the random intensity or statistical parameter of random variable is changed, the stability about stochastic Lotka-Volterra model is different from the deterministic system.展开更多
This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From th...This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lii system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.展开更多
A detailed analysis was carried out on global asymptotic behavior of a kind of stochastic SIRS(susceptible-infective-removed-susceptible)model.This model has been obtained by introducing stochasticity into the origina...A detailed analysis was carried out on global asymptotic behavior of a kind of stochastic SIRS(susceptible-infective-removed-susceptible)model.This model has been obtained by introducing stochasticity into the original deterministic SIRS model via the technique of parameter perturbation which is standard in stochastic population modeling.By making corresponding Lyapunov function and using It formula,the condition for the solution of the model tending to the disease free equilibrium asymptotically was obtained.Under this condition,the epidemics will die out as time goes by.Based on this,almost surely exponential stability was analyzed.展开更多
The global asymptotical stability for a class of stochastic delayed neural networks （SDNNs） with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito＇s differential rule, new d...The global asymptotical stability for a class of stochastic delayed neural networks （SDNNs） with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito＇s differential rule, new delay-dependent stability conditions are derived. All results are expressed in terms of linear matrix inequality （LMI）, and a numerical example is presented to illustrate the correctness and less conservativeness of the proposed method.展开更多
A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of ...A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease.展开更多
In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and g...In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.展开更多
This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such a...This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.展开更多
Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the su...Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.展开更多
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix i...This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.展开更多
Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of the solution...Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of the solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained, The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.展开更多
The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic deriva...The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.展开更多
In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with tin.delays. Based on a Lyapunov-Krasovskii functional and the stochastic stabilit...In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with tin.delays. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived in order to guarantee the global asymptotic convergence of the equilibtium paint in the mean square. Investigation shows that the addressed stochastic highorder delayed neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities （LMIs）. Hence, the global asymptotic stability of the studied stochastic high-order delayed neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.展开更多
In this paper, the problem of state feedback stabilization for stochastic feedforward nonlinear systems with input time-delay is considered for the first time. By introducing a variable transformation, skillfully comb...In this paper, the problem of state feedback stabilization for stochastic feedforward nonlinear systems with input time-delay is considered for the first time. By introducing a variable transformation, skillfully combining the homogeneous domination method, and constructing an appropriate LyapunovKrasovskii functional, a state feedback controller is developed to guarantee the closed-loop system globally asymptotically stable in probability.展开更多
In this paper, we investigate the pth moment uniformly asymptotic stability of impulsive stochastic ftmctional differential systems by extending some Razumikhin-type theorems. Based on the Lyapunov functions and Razum...In this paper, we investigate the pth moment uniformly asymptotic stability of impulsive stochastic ftmctional differential systems by extending some Razumikhin-type theorems. Based on the Lyapunov functions and Razumikhin techniques, some criteria are established and their applications to impulsive stochastic delay systems are proposed. An illustrative example shows the effectiveness of our results.展开更多
In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time.The proof for large deviation ...In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time.The proof for large deviation principle is based on the weak convergence approach.For small time asymptotics we use the exponential equivalence to prove the result.展开更多
基金supported by the National Natural Science Foundation of China(11362001 and 11002001)the Natural Science Foundation of Ningxia Hui Autonomous Region(NZ12210)
文摘The asymptotic stability of a discrete logistic model with random growth coefficient is studied in this paper. Firstly, the discrete logistic model with random growth coefficient is built and reduced into its deterministic equivalent system by orthogonal polynomial approximation. Then, the linear stability theory and the Jury criterion of nonlinear deterministic discrete systems are applied to the equivalent one. At last, by mathematical analysis, we find that the parameter interval for asymptotic stability of nontrivial equilibrium in stochastic logistic system gets smaller as the random intensity or statistical parameters of random variable is increased and the random parameter’s influence on asymptotic stability in stochastic logistic system becomes prominent.
文摘The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system by orthogonal polynomial approximation. Then, the linear stability theory and Routh-Hurwitz criterion for nonlinear deterministic systems are applied to the equivalent one. At last, at the aid of Lyapunov second method, we obtain that as the random intensity or statistical parameter of random variable is changed, the stability about stochastic Lotka-Volterra model is different from the deterministic system.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10902085)
文摘This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lii system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.
基金Foundation of Shanghai for Outstanding Young Teachers in University,China(No.B-5300-08-007)the 085 Knowledge Innovation Project of Shanghai Municipal Education Commission,China(No.Z08509008-01)Humanities and SocialScience Fund General Project of Ministry of Education,China(No.08JA630051)
文摘A detailed analysis was carried out on global asymptotic behavior of a kind of stochastic SIRS(susceptible-infective-removed-susceptible)model.This model has been obtained by introducing stochasticity into the original deterministic SIRS model via the technique of parameter perturbation which is standard in stochastic population modeling.By making corresponding Lyapunov function and using It formula,the condition for the solution of the model tending to the disease free equilibrium asymptotically was obtained.Under this condition,the epidemics will die out as time goes by.Based on this,almost surely exponential stability was analyzed.
基金supported by the National Natural Science Foundation of China(60874114).
文摘The global asymptotical stability for a class of stochastic delayed neural networks （SDNNs） with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito＇s differential rule, new delay-dependent stability conditions are derived. All results are expressed in terms of linear matrix inequality （LMI）, and a numerical example is presented to illustrate the correctness and less conservativeness of the proposed method.
文摘A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease.
文摘In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.
基金The National Natural Science Foundation of China (No.10671078)
文摘This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.
基金Supported by the National Natural Science Founda-tion of China (19531070) and the Major Project Foundation of HubeiProvince Education Department (2004Z001)
文摘Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.
基金This work was supported by the National Natural Science Foundation of China(No.60474013)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050424002)the Doctoral Foundation of Shandong Province (No. 2004BS01010)
文摘This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
基金Project supported by the National Natural Science Foundation of China (Nos.60574025, 60074008)the Natural Science Foundation of Hubei Province of China (No.2004ABA055)
文摘Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of the solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained, The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.
基金supported by the National Natural Science Foundation of China(61273126)the Natural Science Foundation of Guangdong Province(10251064101000008+1 种基金S201210009675)the Fundamental Research Funds for the Central Universities(2012ZM0059)
文摘The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.
文摘In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with tin.delays. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived in order to guarantee the global asymptotic convergence of the equilibtium paint in the mean square. Investigation shows that the addressed stochastic highorder delayed neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities （LMIs）. Hence, the global asymptotic stability of the studied stochastic high-order delayed neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.
基金Supported by National Natural Science Foundation of China(61273125,61473171)Program for the Scientific Research Innovation Team in Colleges and Universities of Shandong ProvinceShandong Provincial Natural Science Foundation(ZR2012FM018)
文摘In this paper, the problem of state feedback stabilization for stochastic feedforward nonlinear systems with input time-delay is considered for the first time. By introducing a variable transformation, skillfully combining the homogeneous domination method, and constructing an appropriate LyapunovKrasovskii functional, a state feedback controller is developed to guarantee the closed-loop system globally asymptotically stable in probability.
基金supported by the National Natural Science Foundation of China(60874114)
文摘In this paper, we investigate the pth moment uniformly asymptotic stability of impulsive stochastic ftmctional differential systems by extending some Razumikhin-type theorems. Based on the Lyapunov functions and Razumikhin techniques, some criteria are established and their applications to impulsive stochastic delay systems are proposed. An illustrative example shows the effectiveness of our results.
基金Research supported in part by NSFC(No.11771037)Key Lab of Random Complex Structures and Data Science,Chinese Academy of ScienceFinancial the DFG through the CRC 1283“Taming uncertainty and profiting from randomness and low regularity in analysis,stochastics and their applications”。
文摘In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time.The proof for large deviation principle is based on the weak convergence approach.For small time asymptotics we use the exponential equivalence to prove the result.
