This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t...This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), and εy′(t)=g(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), where 0<ε1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.展开更多
In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution...In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.展开更多
The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an ...The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the LyapunovKarasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.展开更多
In this paper, topology identification of general weighted complex network with time-varying delay and stochastic perturbation,which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-fe...In this paper, topology identification of general weighted complex network with time-varying delay and stochastic perturbation,which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-feedback control method, the stochastic Lyapunov stability theory and the ito formula, some synchronous criteria are established, which guarantee the asymptotical mean square synchronization of the drive network and the response network with stochastic disturbances, as well as identify the topological structure of the uncertain general drive complex network. Finally, numerical simulations are presented to verify the correctness and effectiveness of the proposed scheme.展开更多
文摘This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), and εy′(t)=g(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), where 0<ε1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
文摘In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.
基金Supported by the National Nature Science Foundation of China (No. 60274007, 60474001)
文摘The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the LyapunovKarasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.
基金Supported by the National Natural Science Foundation of China(60904060and61104127)
文摘In this paper, topology identification of general weighted complex network with time-varying delay and stochastic perturbation,which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-feedback control method, the stochastic Lyapunov stability theory and the ito formula, some synchronous criteria are established, which guarantee the asymptotical mean square synchronization of the drive network and the response network with stochastic disturbances, as well as identify the topological structure of the uncertain general drive complex network. Finally, numerical simulations are presented to verify the correctness and effectiveness of the proposed scheme.
