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
A nonautonomous delayed logistic model with linear feedback regulation is proposed in this paper. Sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic so...A nonautonomous delayed logistic model with linear feedback regulation is proposed in this paper. Sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solution of the model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 SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number is calculated. It is shown that this number characterizes the disease transmission dynamic...A SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number is calculated. It is shown that this number characterizes the disease transmission dynamics: if, there only exists the disease-free equilibrium which is globally asymptotically stable;if, there is a unique endemic equilibrium and the disease persists, sufficient cond- itions are obtained for the global asymptotic stability of the endemic equilibrium.展开更多
In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for ...In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for short) of the model under pulse vaccination and birth pulse is obtained. Based on the Floquet theory and comparison theorem of impulsive differential equations, the global asymptotic stability of the DFPS is given, and sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results.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
We study global asymptotic stability for an SIS epidemic model with maturation delay proposed by K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemi...We study global asymptotic stability for an SIS epidemic model with maturation delay proposed by K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39（4） （1999） 332-352. It is assumed that the population has a nonlinear birth term and disease causes death of infective individuals. By using a monotone iterative method, we establish sufficient conditions for the global stability of an endemic equilibrium when it exists dependently on the monotone property of the birth rate function. Based on the analysis, we further study the model with two specific birth rate functions BI（N） = be-aN and B3（N） = A/N ＋ c, where N denotes the total population. For each model, we obtain the disease induced death rate which guarantees the global stability of the endemic equilibrium and this gives a positive answer for an open problem by X. Q. Zhao and X. Zou, Threshold dynamics in a delayed SIS epidemic model, J. Math. Anal. Appl. 257（2） （2001） 282-291.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A nonautonomous delayed logistic model with linear feedback regulation is proposed in this paper. Sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solution of the model
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 SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number is calculated. It is shown that this number characterizes the disease transmission dynamics: if, there only exists the disease-free equilibrium which is globally asymptotically stable;if, there is a unique endemic equilibrium and the disease persists, sufficient cond- itions are obtained for the global asymptotic stability of the endemic equilibrium.
基金The Fundamental Research Funds for the Central Universities,CHD (300102129202)the NSF (11701041) of China+1 种基金the Natural Science Basic Research Plan (2018JM1011) in Shaanxi Province of ChinaScientific Innovation Practice Project (300103002110) of Postgraduates of Chang’an University
文摘In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for short) of the model under pulse vaccination and birth pulse is obtained. Based on the Floquet theory and comparison theorem of impulsive differential equations, the global asymptotic stability of the DFPS is given, and sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results.
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.
文摘We study global asymptotic stability for an SIS epidemic model with maturation delay proposed by K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39（4） （1999） 332-352. It is assumed that the population has a nonlinear birth term and disease causes death of infective individuals. By using a monotone iterative method, we establish sufficient conditions for the global stability of an endemic equilibrium when it exists dependently on the monotone property of the birth rate function. Based on the analysis, we further study the model with two specific birth rate functions BI（N） = be-aN and B3（N） = A/N ＋ c, where N denotes the total population. For each model, we obtain the disease induced death rate which guarantees the global stability of the endemic equilibrium and this gives a positive answer for an open problem by X. Q. Zhao and X. Zou, Threshold dynamics in a delayed SIS epidemic model, J. Math. Anal. Appl. 257（2） （2001） 282-291.
