CHAOTIFICATION OF LINEAR IMPULSIVE DIFFERENTIAL SYSTEMS WITH APPLICATIONS

Abstract

Chaotification of dynamical systems is a hot topic in the research field of chaos in recent years. Previous studies showed that (even linear) discrete or continuous dynamical systems can be chaotified by designing appropriate controllers. Here, we study chaotification of linear impulsive differential systems. First, we propose a framework for chaotification of general linear impulsive differential systems that can be transformed into discrete maps. Then, we give technical details for how to chaotify several typical linear impulsive differential systems that are actually canonical forms, including how to design appropriate quadratic impulsive controllers, how to find snapback repellers in the Marotto theorem, etc. As one of the main theoretical results, we rigorously prove the existence of chaos in all the considered impulsive systems. In addition, numerical examples are used to verify the theoretical prediction in each case. We are expecting that our proposed approach can have practical applications in the engineering field.