Differential Equation Boundary Value Problem And The Synchronization Of Chaotic Systems Is Studied

AS main one of the branches of nonlinear science, Chaos has became a hot topic of research.For making benefit maximization analysis and forecast of behavior of chaotic systems，we mustfind ways to control chaotic systems. The impulse differential system can relfect the changingrules more accurately by taking the influence of instantaneous mutation into consideration. Inthis paper, we will use a Lyapunov function to prove the impulsive control system is globallyasymptotically synchronous with the corresponding slave system, when the nonlinear part of thechaotic system satisfies some assumption.On the other hand, the theory of impulsive differential equations descirbes processes whichexperience a sudden change of their state at certain moments. A large number of scientific andtechnological results show that impulsive differential equations is a very promising method onbiotechnology, physics, economic, and other important ifelds. The theory of impulsive differentialequations has been emerging as an important area of investigations. It is well known that Kras-’noselskiis ifxed point theorem in a cone has been instrumental in proving the existence of positivesolutions of two-point boundary value problems for second-order differential equations. In thisarticle, we want use this theorem to study a second-order impulsive integro-differential equations.This paper consists of three parts.In chapter1，we ifrst introduce the background.In chapter2，we make an attempt to study synchronization for a class of chaotic system.In chapter3, we are interested in the investigation of the existence of positive solutions of aclass of impulsive integro-differential equation with integral boundary conditions.