The Synchronization Of Coupled Dynamical Systems

Synchronized motion in coupled dynamical systems has attracted much attention over the last few decades,due to the need in achieving a better understanding of this ubiquitous phenomenon in nonlinear science and its applications in such diverse areas as communications,optics,and neurobiological networks.In Chapter 1, we introduce the background of synchronization including a brief introduction of nonlinear sciences and the concept of chaotic synchronization.Chapter 2 is devoted to the discussion of the synchronization of coupled dynamical systems with the external coupling matrices being n × n irreducible circulant real matrices having zero row sum and nonnegative off-diagonal elements and internal coupling matrices being m × m symmetric positive definite matrices. Firstly, we discuss the synchronization of identical coupled systems. Secondly, we discuss the the synchronization of nonidentical coupled systems. Finally, we discuss the synchronization of the coupled systems with external periodic driving.In Chapter 3, we discuss the synchronization of coupled dynamical systems on condition that the external coupling matrices are n × n irreducible symmetric real matrices with zero row sum and nonnegative off-diagonal elements and internal coupling matrices are m × m asymmetric matrices. We describe our approach with a concrete example.Some conclusions and prospects are presented in Chapter 4.