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
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
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 a previous work(2018,Commun.Theor.Phys.70,795–802),a new compartment model for the spreading of rumors was introduced and analyzed.However,only the local asymptotic stability of this model was discussed.In the pre...In a previous work(2018,Commun.Theor.Phys.70,795–802),a new compartment model for the spreading of rumors was introduced and analyzed.However,only the local asymptotic stability of this model was discussed.In the present work,we first provide a rigorous mathematical analysis for the global asymptotic stability(GAS)of the above-mentioned rumor spreading model.By constructing suitable Lyapunov candidate functions,we obtain the GAS of a rumor-free(boundary)equilibrium point and a unique rumor-spreading(positive)equilibrium point.After that,we utilize the approach based on the Lyapunov candidate functions to study the GAS of another rumor spreading model with control strategies,which was proposed in(2022,Physica A 606,128157).As an important consequence,the GAS of the rumor spreading model with control strategies is determined fully without resorting to technical hypotheses used in the benchmark work.Lastly,the theoretical findings are supported by a set of illustrative numerical examples.The obtained results not only improve the ones constructed in the two abovementioned benchmark papers but also can be extended to study the global dynamics of other rumor propagation models in the context of both integer-order and fractional-order derivatives.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
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
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
In this paper, we study a nonautonomous Lotka-Volterra competitive system with infnite delay and feedback controls. By means of a suitable Lyapunov functional, we establish sufcient conditions which guarantee the glob...In this paper, we study a nonautonomous Lotka-Volterra competitive system with infnite delay and feedback controls. By means of a suitable Lyapunov functional, we establish sufcient conditions which guarantee the global asymptotic stability 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
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, 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
In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By u...In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.展开更多
In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent lit...In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.展开更多
A ratio dependent predator-prey system with Holling type Ⅲ functional response is considered. A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle ar...A ratio dependent predator-prey system with Holling type Ⅲ functional response is considered. A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymp- totic stability of the positive equilibrium. The condition under which positive equilibrium is not a hyperbolic equilibrium is investigated using Hopf bifurcation.展开更多
In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-de...In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.展开更多
In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium <span><em>E<...In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium <span><em>E</em></span><sup>*</sup><sub style="margin-left:-6px;">0</sub>, CTL-inactivated infection equilibrium <span><em>E</em></span><sup>*</sup><sub style="margin-left:-6px;">1</sub> and CTL-activated infection equilibrium <span><em>E</em></span><sup>*</sup><sub style="margin-left:-6px;">2</sub>. We prove that in the absence of CTL immune delay, the model has exactly the basic behaviour model, for all positive intracellular delays, the global dynamics are determined by two threshold parameters <em>R</em><sub>0</sub> and <em>R</em><sub>1</sub>, if <em>R</em><sub>0</sub> <span style="font-size:12px;white-space:nowrap;">≤</span> 1, <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>0</sub> </span>is globally asymptotically stable, if <em>R</em><sub>1</sub> <span style="font-size:12px;white-space:nowrap;">≤</span> 1 < <em>R</em><sub>0</sub>, <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>1</sub> </span>is globally asymptotically stable and if <em>R</em><sub>1</sub> >1, <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>2</sub> </span>is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>2</sub> </span>changes completely, although <em>R</em><sub>1</sub> > 1, a Hopf bifurcation at <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>2</sub> </span>is established. In the end, we present some numerical simulations.展开更多
This paper reports the global asymptotic stability of a three-species predator-prey system involving the prey-taxis. With the assumptions, we establish the global asymptotic stability results of its equilibria, respec...This paper reports the global asymptotic stability of a three-species predator-prey system involving the prey-taxis. With the assumptions, we establish the global asymptotic stability results of its equilibria, respectively. Our results illustrate that 1) the global asymptotic stability of the semi-trivial equilibrium does not involve the prey-taxis coefficients χ, ξ;2) the global asymptotic stability of two boundary equilibria relies on a single prey-taxis coefficient χ and ξ, respectively;3) the global asymptotic stability of the unique positive equilibrium depends on two prey-taxis coefficients χ and ξ.展开更多
This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical ...This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.展开更多
In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays (MJSCGNNs) is considered. A novel LMI-based st...In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays (MJSCGNNs) is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen-Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples.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.
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 a previous work(2018,Commun.Theor.Phys.70,795–802),a new compartment model for the spreading of rumors was introduced and analyzed.However,only the local asymptotic stability of this model was discussed.In the present work,we first provide a rigorous mathematical analysis for the global asymptotic stability(GAS)of the above-mentioned rumor spreading model.By constructing suitable Lyapunov candidate functions,we obtain the GAS of a rumor-free(boundary)equilibrium point and a unique rumor-spreading(positive)equilibrium point.After that,we utilize the approach based on the Lyapunov candidate functions to study the GAS of another rumor spreading model with control strategies,which was proposed in(2022,Physica A 606,128157).As an important consequence,the GAS of the rumor spreading model with control strategies is determined fully without resorting to technical hypotheses used in the benchmark work.Lastly,the theoretical findings are supported by a set of illustrative numerical examples.The obtained results not only improve the ones constructed in the two abovementioned benchmark papers but also can be extended to study the global dynamics of other rumor propagation models in the context of both integer-order and fractional-order derivatives.
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.
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 the Foundation of Fujian Education Bureau(No.JA12373)
文摘In this paper, we study a nonautonomous Lotka-Volterra competitive system with infnite delay and feedback controls. By means of a suitable Lyapunov functional, we establish sufcient conditions which guarantee the global asymptotic stability 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.
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].
基金supported in part by JSPS Fellows,No.237213 of Japan Society for the Promotion of Science to the first authorthe Grant MTM2010-18318 of the MICINN,Spanish Ministry of Science and Innovation to the second authorScientific Research (c),No.21540230 of Japan Society for the Promotion of Science to the third author
文摘In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.
基金supported by Scientific Research(c),No.24540219 of Japan Society for the Promotion of Sciencesupported by Grant-in-Aid for Research Activity Start-up,No.25887011 of Japan Society for the Promotion of Science
文摘In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.
文摘A ratio dependent predator-prey system with Holling type Ⅲ functional response is considered. A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymp- totic stability of the positive equilibrium. The condition under which positive equilibrium is not a hyperbolic equilibrium is investigated using Hopf bifurcation.
文摘In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.
文摘In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium <span><em>E</em></span><sup>*</sup><sub style="margin-left:-6px;">0</sub>, CTL-inactivated infection equilibrium <span><em>E</em></span><sup>*</sup><sub style="margin-left:-6px;">1</sub> and CTL-activated infection equilibrium <span><em>E</em></span><sup>*</sup><sub style="margin-left:-6px;">2</sub>. We prove that in the absence of CTL immune delay, the model has exactly the basic behaviour model, for all positive intracellular delays, the global dynamics are determined by two threshold parameters <em>R</em><sub>0</sub> and <em>R</em><sub>1</sub>, if <em>R</em><sub>0</sub> <span style="font-size:12px;white-space:nowrap;">≤</span> 1, <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>0</sub> </span>is globally asymptotically stable, if <em>R</em><sub>1</sub> <span style="font-size:12px;white-space:nowrap;">≤</span> 1 < <em>R</em><sub>0</sub>, <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>1</sub> </span>is globally asymptotically stable and if <em>R</em><sub>1</sub> >1, <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>2</sub> </span>is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>2</sub> </span>changes completely, although <em>R</em><sub>1</sub> > 1, a Hopf bifurcation at <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>2</sub> </span>is established. In the end, we present some numerical simulations.
文摘This paper reports the global asymptotic stability of a three-species predator-prey system involving the prey-taxis. With the assumptions, we establish the global asymptotic stability results of its equilibria, respectively. Our results illustrate that 1) the global asymptotic stability of the semi-trivial equilibrium does not involve the prey-taxis coefficients χ, ξ;2) the global asymptotic stability of two boundary equilibria relies on a single prey-taxis coefficient χ and ξ, respectively;3) the global asymptotic stability of the unique positive equilibrium depends on two prey-taxis coefficients χ and ξ.
基金supported by the National Natural Science Foundation of China(10971166,10901131)the National High Technology Research and Development Program of China(863 Program,2009AA01A135)the Natural Science Foundation of Xinjiang Province(2010211B04)
文摘This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.
基金supported by DST Project(Grant No.SR/FTP/MS-039/2011)
文摘In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays (MJSCGNNs) is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen-Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples.