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
Sufficient conditions to guarantee the existence and global exponential stability of periodic solutions of a Cohen-Grossberg-type BAM neural network are established by suitable mathematical transformation.
A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stag...A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stages:immature and mature.The global attractiveness of the pest-eradication periodic solution is discussed,and sufficient condition is obtained for the permanence of the system.Further,numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics,which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.展开更多
The concept of relative t-designs for Q-polynomial association schemes is due to Delsarte(Philips Res Rep 32: 373C411, 1997). In this paper, we discuss the Fisher type lower bounds of tight relative 6-designs very exp...The concept of relative t-designs for Q-polynomial association schemes is due to Delsarte(Philips Res Rep 32: 373C411, 1997). In this paper, we discuss the Fisher type lower bounds of tight relative 6-designs very explicitly for binary Hamming association schemes H(n, 2).展开更多
In this paper, an SIRS epidemic model with time delay and vaccination is investigated. By analyzing the corresponding characteristic equation, the local stability of diseasefree equilibrium of the model is established...In this paper, an SIRS epidemic model with time delay and vaccination is investigated. By analyzing the corresponding characteristic equation, the local stability of diseasefree equilibrium of the model is established. By constructing Lyapunov functional, sufficient conditions are established for the local stability of an endemic equilibrium of the model. Further, a threshold value is obtained. By using comparison arguments, it is proved when the threshold value is less than unity, the diseasefree equilibrium is globally asymptoti cally stable. When the threshold value is greater than unity, by using an iteration scheme and by constructing appropriate Lyapunov functional, respectively, sufficient conditions are derived for the global stability of the endemic equilibrium of the model. Numerical simulations are carried out to illustrate the theoretical results.展开更多
A stage-structured predator-prey system with impulsive effect and Holling type-II functional response is investigated. By the Floquet theory and small amplitude perturbation skills, it is proved that there exists a gl...A stage-structured predator-prey system with impulsive effect and Holling type-II functional response is investigated. By the Floquet theory and small amplitude perturbation skills, it is proved that there exists a global stable pest-eradication periodic solution when the impulsive period is less than some critical values. Farther, the conditions for the permanence of system are established. Numerical simulations are carried out to illustrate the impulsive effect on the dynamics of the system.展开更多
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.
文摘Sufficient conditions to guarantee the existence and global exponential stability of periodic solutions of a Cohen-Grossberg-type BAM neural network are established by suitable mathematical transformation.
基金Foundation item： Supported by the NNSF of China（11071254） Supported by the Science Foundation of Mechanical Engineering College（YJJXMll004）
文摘A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stages:immature and mature.The global attractiveness of the pest-eradication periodic solution is discussed,and sufficient condition is obtained for the permanence of the system.Further,numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics,which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.
基金Supported by the Natural Science Foundation of Hebei Province（A2013408009） Sup- ported by the Specialized Research Fund for the Doctoral Program of Higher Education（20121303110005）+1 种基金 Supported by the Natural Science Foundation of Hebei Education Department（ZH2012082） Supported by the Foundation of Langfang Teachers University（LSBS201205）
文摘The concept of relative t-designs for Q-polynomial association schemes is due to Delsarte(Philips Res Rep 32: 373C411, 1997). In this paper, we discuss the Fisher type lower bounds of tight relative 6-designs very explicitly for binary Hamming association schemes H(n, 2).
文摘In this paper, an SIRS epidemic model with time delay and vaccination is investigated. By analyzing the corresponding characteristic equation, the local stability of diseasefree equilibrium of the model is established. By constructing Lyapunov functional, sufficient conditions are established for the local stability of an endemic equilibrium of the model. Further, a threshold value is obtained. By using comparison arguments, it is proved when the threshold value is less than unity, the diseasefree equilibrium is globally asymptoti cally stable. When the threshold value is greater than unity, by using an iteration scheme and by constructing appropriate Lyapunov functional, respectively, sufficient conditions are derived for the global stability of the endemic equilibrium of the model. Numerical simulations are carried out to illustrate the theoretical results.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1067120910926064)
文摘A stage-structured predator-prey system with impulsive effect and Holling type-II functional response is investigated. By the Floquet theory and small amplitude perturbation skills, it is proved that there exists a global stable pest-eradication periodic solution when the impulsive period is less than some critical values. Farther, the conditions for the permanence of system are established. Numerical simulations are carried out to illustrate the impulsive effect on the dynamics of the system.
