Abstract
The generalized synchronization of the complex network consisting of nodes being the chaotic systems via the auxiliary system approach is studied here. More specifically, the applicability of the auxiliary system approach to detect the generalized synchronization in the complex network consisting of unidirectional coupled chaotic systems in the cyclic chain is investigated. Such a complex network has the so-called ring topology. It is shown that the auxiliary system approach is useful for this purpose. The presented analysis is supported by the numerical simulations as well.
Highlights
Complex networks have been studied within many different branches of science [Chen et al, 2014]
The main contribution of the present paper is the study of the generalized synchronization phenomenon of a class of complex network where all nodes are identical chaotic systems with different control parameters and initial conditions
The motivation of the current research is to show that the auxiliary system approach can be used to detect the generalized synchronization phenomena in the complex network with unidirectional coupling between nodes and ring topology
Summary
Complex networks have been studied within many different branches of science [Chen et al, 2014]. In [Abarbanel et al, 1996], the so-called auxiliary system approach to detect the GS was introduced In this context, the main contribution of the present paper is the study of the generalized synchronization phenomenon of a class of complex network where all nodes are identical chaotic systems with different control parameters and initial conditions. The motivation of the current research is to show that the auxiliary system approach can be used to detect the generalized synchronization phenomena in the complex network with unidirectional coupling between nodes and ring topology. The complex network studied here consist of the nodes being the so-called generalized Lorenz system (GLS) It was already shown in [Celikovskyand Chen, 2005] that two GLS’s, though both being three-dimensional systems, with the master-slave structure can be identically synchronized using the single scalar connection only.
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