Competition between chaos control and chaos synchronization in small sized networks

Abstract

Control and synchronization of chaotic systems have been two important issues of investigation in the eld of chaotic dynamics since early 1990s. Stabilization of chaotic systems at an unstable periodic orbit (UPO) via small parameter perturbations using local linear feedback proposed by Ott, Grebogi and Yorke (OGY method) is one of the earliest and best known techniques for chaos control and has numerous applications, modi cations and extensions in the literature. On the other hand, synchronizability of coupled chaotic systems, which exhibit the so called decomposability property, has been demonstrated by Pecora and Carroll (PC-decomposition) in 1990, and has paved the way for diverse studies and applications of chaos synchronization using di erent con gurations and coupling schemes ever since. In this thesis, an original investigation is conducted where a small number of identical chaotic systems stabilized at distinct UPOs by a modi ed version of the OGY method are coupled according to a selective coupling strategy such that the two tendencies, i. e. the tendency of each system to follow its own distinct UPO and the tendency of the coupled systems to synchronize, compete. It is also studied how this competition can be in uenced by an external static disturbance that e ects all systems in the same manner.