Collective Behavior-I: Synchronization in Hyperchaotic Time-Delayed Oscillators Coupled Through a Common Environment

Abstract

Collective behaviors of coupled dynamical systems are of significant interest in the field of physical and biological sciences, and engineering [96]. The prominent collective behaviors that occur in periodic and chaotic systems are synchronization and phase locking [96], oscillation suppression [10, 15, 16, 47, 63, 112], chimera states [9, 91, 113], etc. We have already discussed in Chap. 1 that synchronization of chaos in time-delayed chaotic system was reported much later by Pyragas [100] (1998) than its discovery in low-dimensional chaotic systems [93] (in 1990). In all the research works discussed in Chap. 1 (Sect. 1.2, p. 6), the coupling schemes were essentially the direct coupling, i.e., either unidirectional coupling or bidirectional coupling , where either of the two coupled systems or both the systems directly affect the dynamics of each other.