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 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
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
Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network mode...Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is ad- vanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).展开更多
In this paper a class of cooperative Lotka-Volterra population system with time delay is considered. Some sufficient conditions on the existence and globally asymptotically stability for the asymptotically periodic so...In this paper a class of cooperative Lotka-Volterra population system with time delay is considered. Some sufficient conditions on the existence and globally asymptotically stability for the asymptotically periodic solution of the system are established by using the Lyapunov function method and the method given in Fengying Wei and Wang Ke (Applied Mathematics and Computation 182 (2006) 161-165).展开更多
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 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
In the paper, we obtain new sufficient conditions ensuring existence, uniqueness, and asymptotic stability of the equilibrium point for delayed neural network via nonsmooth analysis, which makes use of the Lipschitz p...In the paper, we obtain new sufficient conditions ensuring existence, uniqueness, and asymptotic stability of the equilibrium point for delayed neural network via nonsmooth analysis, which makes use of the Lipschitz property of the functions. Based on this tool of nonsmooth analysis, we first obtain a couple of general results concerning the existence and uniqueness of the equilibrium point. Then we drive some new sufficient conditions ensuring global asymptotic stability of the equilibrium point. Finally, there are the illustrative examples feasibility and effectiveness of our results. Throughout our paper, the activation function is a more general function which has a wide application.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
The difference equation △xn＋ pnxn-k = f（n,xn-1,...,xn-1m）, n = 0, 1,2,.. is considered, where {pn} is a sequence of nonnegative real numbers, m ∈ {1, 2, ,... }, k,l1,..., lm ∈ {0, 1, 2,,... }. Some sufficient co...The difference equation △xn＋ pnxn-k = f（n,xn-1,...,xn-1m）, n = 0, 1,2,.. is considered, where {pn} is a sequence of nonnegative real numbers, m ∈ {1, 2, ,... }, k,l1,..., lm ∈ {0, 1, 2,,... }. Some sufficient conditions for the global asymptotic stability of zero solution of the equation are obtained.展开更多
By using a criterion for asymptotic stability in Banach space BC, a group of sufficient condi-tioas for a dynamical model with infinite delay which is derived from hematology were obtained, which refined the result in...By using a criterion for asymptotic stability in Banach space BC, a group of sufficient condi-tioas for a dynamical model with infinite delay which is derived from hematology were obtained, which refined the result in the reference [ 10] got by the second author herself.展开更多
In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kr...In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kravsovskii functional, model transformation and some analysis techniques. The criterion of stability depends on the impulse and the bounds of the leakage time-varying delay and its derivative, and is presented in terms of a linear matrix inequality (LMI).展开更多
This paper discussed the stability of model of an age structured population systems,proved that the equilibrium solution systems is globally asymptotically stable.
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
There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works conc...There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.展开更多
A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obta...A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.展开更多
In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no end...In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point （if it exists） is globally stable with a respect ＂weak delay＂. Some known results are generalized.展开更多
In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch in...In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].展开更多
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 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 (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Project (No. 60074008) supported by the National Natural Science Foundation of China
文摘Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is ad- vanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).
文摘In this paper a class of cooperative Lotka-Volterra population system with time delay is considered. Some sufficient conditions on the existence and globally asymptotically stability for the asymptotically periodic solution of the system are established by using the Lyapunov function method and the method given in Fengying Wei and Wang Ke (Applied Mathematics and Computation 182 (2006) 161-165).
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.
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.
文摘In the paper, we obtain new sufficient conditions ensuring existence, uniqueness, and asymptotic stability of the equilibrium point for delayed neural network via nonsmooth analysis, which makes use of the Lipschitz property of the functions. Based on this tool of nonsmooth analysis, we first obtain a couple of general results concerning the existence and uniqueness of the equilibrium point. Then we drive some new sufficient conditions ensuring global asymptotic stability of the equilibrium point. Finally, there are the illustrative examples feasibility and effectiveness of our results. Throughout our paper, the activation function is a more general function which has a wide application.
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].
基金Supported by Natural Science Foundaton of Henan Providence(0111051200)
文摘The difference equation △xn＋ pnxn-k = f（n,xn-1,...,xn-1m）, n = 0, 1,2,.. is considered, where {pn} is a sequence of nonnegative real numbers, m ∈ {1, 2, ,... }, k,l1,..., lm ∈ {0, 1, 2,,... }. Some sufficient conditions for the global asymptotic stability of zero solution of the equation are obtained.
基金Supported by the Natural Science Foundation of Guangdong Province(011471)Supported by the Education Bureau(0120)
文摘By using a criterion for asymptotic stability in Banach space BC, a group of sufficient condi-tioas for a dynamical model with infinite delay which is derived from hematology were obtained, which refined the result in the reference [ 10] got by the second author herself.
文摘In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kravsovskii functional, model transformation and some analysis techniques. The criterion of stability depends on the impulse and the bounds of the leakage time-varying delay and its derivative, and is presented in terms of a linear matrix inequality (LMI).
文摘This paper discussed the stability of model of an age structured population systems,proved that the equilibrium solution systems is globally asymptotically stable.
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.
文摘There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.
文摘A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.
基金This work is supported by the National Sciences Foundation of China (10471040)the Youth Science Foundations of Shanxi Province (20021003).
文摘In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point （if it exists） is globally stable with a respect ＂weak delay＂. Some known results are generalized.
基金supported by Japan Society for the Promotion of Science (Grant Scientific Research (c), No. 24540219 to the first author, JSPS Fellows, No.237213 to the second author, and No. 222176 to the third author)
文摘In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].
