New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous differ...New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.展开更多
The Control of a hyperchaotic discrete system is investigated, A time-varying feedback control law is established on the base of local linearization. The Liapunov direct method is applied to estimate the neighborhood ...The Control of a hyperchaotic discrete system is investigated, A time-varying feedback control law is established on the base of local linearization. The Liapunov direct method is applied to estimate the neighborhood in which the control law can be effectively used. Numerical examples are presented to demonstrate the applications of the control law to solve the problem of stabilizing unstable periodic orbits and the problem of tracking an arbitrarily given periodic orbit.展开更多
This paper considers the stabilily of the Korteweg-de Vries solitary wave solutionwith respect to infinitesmal dislurbance. It is found that the Korteweg-de Vries solitarywave solulion. is unstable in the Liapunov sense.
文摘New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.
文摘The Control of a hyperchaotic discrete system is investigated, A time-varying feedback control law is established on the base of local linearization. The Liapunov direct method is applied to estimate the neighborhood in which the control law can be effectively used. Numerical examples are presented to demonstrate the applications of the control law to solve the problem of stabilizing unstable periodic orbits and the problem of tracking an arbitrarily given periodic orbit.
文摘This paper considers the stabilily of the Korteweg-de Vries solitary wave solutionwith respect to infinitesmal dislurbance. It is found that the Korteweg-de Vries solitarywave solulion. is unstable in the Liapunov sense.
