Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two o...Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two open problems and extend some known results.展开更多
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their...This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.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
The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature...The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature is low, around 30˚C, the hatchlings are all females. Higher temperature, around 34˚C, hatch all males. This study was made to consider the asymptotic stability of a positive equilibrium point in a nonlinear discrete model of the basic nesting population model, which is described in three-region depending on the temperature of egg incubation. This model is based on key life-historical data and Murray’s research. To study above, we have applied the classical linearization method and P. Cull’s method and moreover, we employ non-standard discretization methods for later our Equations (6)-(8) and (15).展开更多
In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start wi...In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.展开更多
A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derive...A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.展开更多
The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of ...The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.展开更多
In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributio...In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributions of the solution. We prove that the densities can converge in L1 to an invariant density.展开更多
In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., ...In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., where a∈ [0 ,∞ ) and the initial values x- 2 ,x- 1,x0 ∈ (0 ,∞ ) .As a special case,a conjecture by Ladas is confirmed.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
It has been recently found that many models were established with the aid of fractional derivatives, such as viscoelastic systems, colored noise, electrode-electrolyte polarization, dielectric polarization, boundary l...It has been recently found that many models were established with the aid of fractional derivatives, such as viscoelastic systems, colored noise, electrode-electrolyte polarization, dielectric polarization, boundary layer effects in ducts, electromagnetic waves, quantitative finance, quantum evolution of complex systems, and fractional kinetics. In this paper, the asymptotical stability of higher-dimensional linear fractional differential systems with the Riemann-Liouville fractional order and Caputo fractional order were studied. The asymptotical stability theorems were also derived.展开更多
In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one-dimensional system of the rudiating gas. By considering the initial data as a small disturbances ...In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one-dimensional system of the rudiating gas. By considering the initial data as a small disturbances of rarefaction wave of inviscid Burgers equation, the global existence of the solution to the corresponding Cauchy problem and asymptotic stability of rarefaction wave is proved. The analysis is based on a priori estimates and L^2-energy method.展开更多
In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in ...In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.展开更多
The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differen...The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.展开更多
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 global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the conditio...The global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the condition for global uniformly asymptotically stable are given. A strict Lyapunov function for the flow of a competitive neural system with different time scales and delay is presented. Based on the function, the global uniform asymptotic stability of the equilibrium point can be proved.展开更多
We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture.When the corresponding Riemann problem for the Euler system ad...We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture.When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave,it is shown that the viscous contact wave which corresponds to the contact discontinuity is asymptotically stable,provided the strength of contact discontinuity and the initial perturbation are suitably small.We apply the approach introduced in Huang,Li and Matsumura(2010)[1]and the elemen tary L2-energy met hods.展开更多
This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel d...This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This criterion is expressed in terms of linear matrix inequalities (LMIs), which can be easily checked by utilizing the recently developed algorithms for solving LMIs. Examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed condition.展开更多
Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix...Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality(LMI) conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.展开更多
In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results c...In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results completely solve an open problem and some conjectures proposed in[1,2,3,4].展开更多
文摘Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two open problems and extend some known results.
文摘This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.
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.
文摘The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature is low, around 30˚C, the hatchlings are all females. Higher temperature, around 34˚C, hatch all males. This study was made to consider the asymptotic stability of a positive equilibrium point in a nonlinear discrete model of the basic nesting population model, which is described in three-region depending on the temperature of egg incubation. This model is based on key life-historical data and Murray’s research. To study above, we have applied the classical linearization method and P. Cull’s method and moreover, we employ non-standard discretization methods for later our Equations (6)-(8) and (15).
文摘In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.
文摘A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.
文摘The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.
基金supported by Program for Changjiang Scholars and Innovative Research Team in University,NSFC of China(11371085 and 11201008)the Ph.D.Programs Foundation of Ministry of China(200918)
文摘In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributions of the solution. We prove that the densities can converge in L1 to an invariant density.
基金Supported by the National Natural Science Foundation of China(1 0 0 71 0 2 2 ) Mathematical TianyuanFoundation of China(TY1 0 0 2 6 0 0 2 - 0 1 - 0 5 - 0 3 ) Shanghai Priority Academic Discipline Foundation
文摘In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., where a∈ [0 ,∞ ) and the initial values x- 2 ,x- 1,x0 ∈ (0 ,∞ ) .As a special case,a conjecture by Ladas is confirmed.
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.
文摘It has been recently found that many models were established with the aid of fractional derivatives, such as viscoelastic systems, colored noise, electrode-electrolyte polarization, dielectric polarization, boundary layer effects in ducts, electromagnetic waves, quantitative finance, quantum evolution of complex systems, and fractional kinetics. In this paper, the asymptotical stability of higher-dimensional linear fractional differential systems with the Riemann-Liouville fractional order and Caputo fractional order were studied. The asymptotical stability theorems were also derived.
基金The research was supported by three grants from the Key Project of the Natural Science Foundation of China (10431060)the Key Project of Chinese Ministry of Education (104128)the South-Central University For Nationalities Natural Science Foundation of China (YZY05008)
文摘In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one-dimensional system of the rudiating gas. By considering the initial data as a small disturbances of rarefaction wave of inviscid Burgers equation, the global existence of the solution to the corresponding Cauchy problem and asymptotic stability of rarefaction wave is proved. The analysis is based on a priori estimates and L^2-energy method.
基金This project was supported by the National Natural Science Foundation of China (60274007) NSERC-Canada.
文摘In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.
基金Project supported by the National Natural Science Foundation of China (No.10571078)the Natural Science Foundation of Gansu Province of China (No.3ZX062-B25-012)
文摘The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.
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 global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the condition for global uniformly asymptotically stable are given. A strict Lyapunov function for the flow of a competitive neural system with different time scales and delay is presented. Based on the function, the global uniform asymptotic stability of the equilibrium point can be proved.
基金supported by the National Natural Science Foundation of China(11871341).
文摘We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture.When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave,it is shown that the viscous contact wave which corresponds to the contact discontinuity is asymptotically stable,provided the strength of contact discontinuity and the initial perturbation are suitably small.We apply the approach introduced in Huang,Li and Matsumura(2010)[1]and the elemen tary L2-energy met hods.
基金supported by National Natural Science Foundation of China (No. 60674027, 60875039, 60904022 and 60974127)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050446001)+2 种基金China Postdoctoral Science Foundation(No. 20070410336)Postdoctoral Foundation of Jiangsu Province(No. 0602042B)Scientific Research Foundation of Qufu Normal University
文摘This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This criterion is expressed in terms of linear matrix inequalities (LMIs), which can be easily checked by utilizing the recently developed algorithms for solving LMIs. Examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed condition.
基金Supported by the National Natural Science Foundation of China (6067402760875039)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education (20050446001)Scientific Research Foundation of Qufu Normal University
文摘Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality(LMI) conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.
基金the National Natural Science Foundation of China(61473340)the Distinguished Professor Foundation of Qianjiang Scholar in Zhejiang Province+1 种基金the National Natural Science Foundation of Zhejiang Province(LQ13A010019)the National Natural Science Foundation of Zhejiang University of Science and Technology(F701108G14).
文摘In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results completely solve an open problem and some conjectures proposed in[1,2,3,4].