Synchronization and adaptive synchronization of Morse oscillator with periodic forced section is investigated in this paper. Backstepping design is a recursive procedure that combines the choice of Lyapunov function w...Synchronization and adaptive synchronization of Morse oscillator with periodic forced section is investigated in this paper. Backstepping design is a recursive procedure that combines the choice of Lyapunov function with the design of controller. The proposed approaches offers a syetematic design procedure for synchronization and adaptive synchronization of a large class of continuous-time chaotic systems in the chaos research literature. Simulation results are presented to show the effectiveness of the approaches.展开更多
This paper is devoted to studying the asymptotic stability of retarded nonlinear functional differential equations by the method of Lyapunov functionals. Under the as-sumption that there exists a positive definite tim...This paper is devoted to studying the asymptotic stability of retarded nonlinear functional differential equations by the method of Lyapunov functionals. Under the as-sumption that there exists a positive definite time-invariant Lyapunov functional with negative semi-definite derivative, we focus on the extra conditions to guarantee the asymptotic stability, and present a new criterion, which is less conservative than the classical one. Finally, an example is given to illustrate the effectiveness of the result.展开更多
We introduce the class-age-dependent rates of the infected and vaccinated class in the compartmental model of dengue transmission. An age-structured host-vector interac- tion model incorporating vaccination effects is...We introduce the class-age-dependent rates of the infected and vaccinated class in the compartmental model of dengue transmission. An age-structured host-vector interac- tion model incorporating vaccination effects is formulated and analyzed for the spread of dengue. Moreover, the basic reproduction number is derived, which serves as a thresh- old value determining the stability of the equilibrium points. By constructing suitable Lyapunov functional, the global asymptotic stability of the equilibria of the model is established in terms of the basic reproduction number. In particular, the disease-free equilibrium of the model is globally asymptotically stable if the basic reproduction num- ber is less than one, while the disease persists and the unique endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than one. The analysis of our model indicates that our model is realistic to give a hint to control the transmission of dengue. Furthermore, it follows from the formulation of the infection-free equilibrium of susceptible humans So and the basic reproduction number R0 that both of them are decreasing with respect to the vaccination parameter ~bh, which indicates that appropriate vaccinating program may contribute to prevent the transmission of Dengue disease.展开更多
基金This work is supported by Research Fund Project of Heze University under Grant: XY05SX01.
文摘Synchronization and adaptive synchronization of Morse oscillator with periodic forced section is investigated in this paper. Backstepping design is a recursive procedure that combines the choice of Lyapunov function with the design of controller. The proposed approaches offers a syetematic design procedure for synchronization and adaptive synchronization of a large class of continuous-time chaotic systems in the chaos research literature. Simulation results are presented to show the effectiveness of the approaches.
基金supported by the National Basic Research Program of China (973 Program,Grant No.2005CB321902)the National Natural Science Foundation of China (Grant No.60473109+1 种基金No.60374001)the Doctor Fund of Ministry of Education of China (No.20030006003)
文摘This paper is devoted to studying the asymptotic stability of retarded nonlinear functional differential equations by the method of Lyapunov functionals. Under the as-sumption that there exists a positive definite time-invariant Lyapunov functional with negative semi-definite derivative, we focus on the extra conditions to guarantee the asymptotic stability, and present a new criterion, which is less conservative than the classical one. Finally, an example is given to illustrate the effectiveness of the result.
文摘We introduce the class-age-dependent rates of the infected and vaccinated class in the compartmental model of dengue transmission. An age-structured host-vector interac- tion model incorporating vaccination effects is formulated and analyzed for the spread of dengue. Moreover, the basic reproduction number is derived, which serves as a thresh- old value determining the stability of the equilibrium points. By constructing suitable Lyapunov functional, the global asymptotic stability of the equilibria of the model is established in terms of the basic reproduction number. In particular, the disease-free equilibrium of the model is globally asymptotically stable if the basic reproduction num- ber is less than one, while the disease persists and the unique endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than one. The analysis of our model indicates that our model is realistic to give a hint to control the transmission of dengue. Furthermore, it follows from the formulation of the infection-free equilibrium of susceptible humans So and the basic reproduction number R0 that both of them are decreasing with respect to the vaccination parameter ~bh, which indicates that appropriate vaccinating program may contribute to prevent the transmission of Dengue disease.
