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
A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions,and...A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions,and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.展开更多
According to the epidemic state, propagation mode and transformation between HBV infection states,the Hepatitis B Virus （HBV） infection with impulsive vaccination and time delay are modelled and analyzed. The contro...According to the epidemic state, propagation mode and transformation between HBV infection states,the Hepatitis B Virus （HBV） infection with impulsive vaccination and time delay are modelled and analyzed. The control methods of impulsive vaccination and active therapy are adopted. By using comparative theorem of impulsive differential equation, the sufficient conditions that Hepatitis B Virus will be eliminated eventually or be persistent are derived.展开更多
In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but...In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.展开更多
Due to the appearance and the study of the ornithopter and flexible-wing micro air vehicles, etc., the time-varying systems become more and more important and ubiquitous in the study of the mechanics. In this letter, ...Due to the appearance and the study of the ornithopter and flexible-wing micro air vehicles, etc., the time-varying systems become more and more important and ubiquitous in the study of the mechanics. In this letter, the sufficient conditions of the uniform asymptotic stability are first presented for the delayed time-varying linear differential equations with any time delay by employing the Dini derivative, Lozinskii measure and the generalized scalar Halanay delayed differential inequality. They are especially based on the estimation of the arbitrary solutions but not the fundamental solution matrix since their solutions＇ space is infinite-dimensional. Then some sufficient conditions of the stability, asymptotic stability and uniform asymptotic stability of the delayed time-varying linear system with a sufficiently small time delay are reported by employing Taylor expansion and Dini derivative. It implies that these stabilities can be guaranteed by the Lozinskii measure of the matrix composing of the time delay and the coefficient matrices of the system.展开更多
The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems （NCSs）. Based on Lyapunov stability theorem combined with improved Razumikhin technique, the su...The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems （NCSs）. Based on Lyapunov stability theorem combined with improved Razumikhin technique, the sufficient conditions of asymptotic stability for the system are derived. With the proposed method, the estimate of maximum allowable delay bound （MADB） for linear networked control system is also given. Compared to the other methods, the proposed method gives a much less conservative MADB and more general results. Numerical examples and some simulations are worked out to demonstrate the effectiveness and performance of the proposed method.展开更多
In this paper a delayed mathematical model for tumor growth under the action of external inhibitors is studied. The delay represents the time taken for cells to undergo mitosis. External inhibitor means that an inhibi...In this paper a delayed mathematical model for tumor growth under the action of external inhibitors is studied. The delay represents the time taken for cells to undergo mitosis. External inhibitor means that an inhibitor is either developed from the immune system of the body or administered by medical treatment to distinguish with that secreted by tumor itself. Non-negativity of solutions is studied. Local and global stabilities of the stationary solutions are proved for some parameter values. The analysis of the effect of inhibitor＇s parameters on tumor＇s growth is presented. The results show that dynamical behavior of solutions of this model is similar to that of solutions for corresponding nondelayed model for some parameter values.展开更多
The uniform permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type N-species competitive systems with diffusion and delays are investigated. It is shown that the system is uniform...The uniform permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type N-species competitive systems with diffusion and delays are investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and new sufficient conditions are obtained for the global asymptotic stability of the unique positive almost periodic solution of the system.展开更多
A new epidemic SIRS model with discrete delay on scale-free network is presented. We give the formula of the basic reproductive number for the model and prove that the disease dies out when the basic reproductive numb...A new epidemic SIRS model with discrete delay on scale-free network is presented. We give the formula of the basic reproductive number for the model and prove that the disease dies out when the basic reproductive number is less than unity, while the disease is uniformly persistent when the basic reproductive number is more than unity. Numerical simulations are given to demonstrate the main results.展开更多
An SIS model with periodic maximum infectious force, recruitment rate and the removal rate of the infectives has been investigated in this article. Sufficient conditions for the permanence and extinction of the diseas...An SIS model with periodic maximum infectious force, recruitment rate and the removal rate of the infectives has been investigated in this article. Sufficient conditions for the permanence and extinction of the disease are obtained. Furthermore, the existence and global stability of positive periodic solution are established. Finally, we present a procedure by which one can control the parameters of the model to keep the infectives stay eventually in a desired set.展开更多
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.
文摘A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions,and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.
基金supported by the Fundamental Research Funds for the Central Universities,China University of Geosciences (Wuhan) CUGL1002382011CB710600 (973 Program)
文摘According to the epidemic state, propagation mode and transformation between HBV infection states,the Hepatitis B Virus （HBV） infection with impulsive vaccination and time delay are modelled and analyzed. The control methods of impulsive vaccination and active therapy are adopted. By using comparative theorem of impulsive differential equation, the sufficient conditions that Hepatitis B Virus will be eliminated eventually or be persistent are derived.
基金This work is supported by the Foundation of Ability Person of Fuzhou University under the grant 0030824228 andthe Foundation of Developing Science and Technology of Fuzhou University under the grant 2003-QX-21 and the Foundation of Fujian Education Bur
文摘In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.
基金supported by the National Natural Science Foundation of China(10702065 and 11372282)
文摘Due to the appearance and the study of the ornithopter and flexible-wing micro air vehicles, etc., the time-varying systems become more and more important and ubiquitous in the study of the mechanics. In this letter, the sufficient conditions of the uniform asymptotic stability are first presented for the delayed time-varying linear differential equations with any time delay by employing the Dini derivative, Lozinskii measure and the generalized scalar Halanay delayed differential inequality. They are especially based on the estimation of the arbitrary solutions but not the fundamental solution matrix since their solutions＇ space is infinite-dimensional. Then some sufficient conditions of the stability, asymptotic stability and uniform asymptotic stability of the delayed time-varying linear system with a sufficiently small time delay are reported by employing Taylor expansion and Dini derivative. It implies that these stabilities can be guaranteed by the Lozinskii measure of the matrix composing of the time delay and the coefficient matrices of the system.
基金supported by Hi-Tech Research and Development (863) Program of China (No.2006AA04Z207)Research Fund for Doctorial Programof Higher Education of China (No.20060006018)+1 种基金International Cooperation Program of Science and Technology of China (No.2007DFA11530)the National Natural Science Foundation of China (No.60875072)
文摘The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems （NCSs）. Based on Lyapunov stability theorem combined with improved Razumikhin technique, the sufficient conditions of asymptotic stability for the system are derived. With the proposed method, the estimate of maximum allowable delay bound （MADB） for linear networked control system is also given. Compared to the other methods, the proposed method gives a much less conservative MADB and more general results. Numerical examples and some simulations are worked out to demonstrate the effectiveness and performance of the proposed method.
文摘In this paper a delayed mathematical model for tumor growth under the action of external inhibitors is studied. The delay represents the time taken for cells to undergo mitosis. External inhibitor means that an inhibitor is either developed from the immune system of the body or administered by medical treatment to distinguish with that secreted by tumor itself. Non-negativity of solutions is studied. Local and global stabilities of the stationary solutions are proved for some parameter values. The analysis of the effect of inhibitor＇s parameters on tumor＇s growth is presented. The results show that dynamical behavior of solutions of this model is similar to that of solutions for corresponding nondelayed model for some parameter values.
基金This research is supported by the National Natural Science Foundation of China(10171056).
文摘The uniform permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type N-species competitive systems with diffusion and delays are investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and new sufficient conditions are obtained for the global asymptotic stability of the unique positive almost periodic solution of the system.
文摘A new epidemic SIRS model with discrete delay on scale-free network is presented. We give the formula of the basic reproductive number for the model and prove that the disease dies out when the basic reproductive number is less than unity, while the disease is uniformly persistent when the basic reproductive number is more than unity. Numerical simulations are given to demonstrate the main results.
基金Partially supported by the National Nature Science Foundation of China (No.19971066)the Youth Sciences Foundation of Shanxi Province (No.20021003).
文摘An SIS model with periodic maximum infectious force, recruitment rate and the removal rate of the infectives has been investigated in this article. Sufficient conditions for the permanence and extinction of the disease are obtained. Furthermore, the existence and global stability of positive periodic solution are established. Finally, we present a procedure by which one can control the parameters of the model to keep the infectives stay eventually in a desired set.
