Inapplicability of an auxiliary-system approach to chaotic oscillators with mutual-type coupling and complex networks

Abstract

The auxiliary system approach being de facto the standard for the study of generalized synchronization in the unidirectionally coupled chaotic oscillators is also widely used to examine the mutually coupled systems and networks of nonlinear elements with the complex topology of links between nodes. In this Brief Report we illustrate by two simple counterexamples that the auxiliary-system approach gives incorrect results for the mutually coupled oscillators and therefore to study the generalized synchronization this approach may be used only for the drive-response configuration of nonlinear oscillators and networks.