Dynamics and synchronization of a complex-valued star network

Abstract

Complex networks have been extensively investigated in recent years. However, the dynamics, especially chaos and bifurcation, of the complex-valued complex network are rarely studied. In this paper, a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling. By the aid of bifurcation diagram, Lyapunov exponent spectrum and phase portrait in this study, chaos, hyper-chaos, and multi-existing chaotic attractors are observed from the star network, although there are only periodic states in a complex-valued van der Pol oscillator. Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size, the larger the parameter range within the chaotic (hyper-chaotic) region. It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network, and it always evolves to chaos directly from period-1 and quasi-periodic states, respectively. Moreover, the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network, which is a symmetrybreaking phenomenon.

Dynamical analysis, geometric control and digital hardware implementation of a complex-valued laser system with a locally active memristor

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“…It can induce switching between different coexistence states or shift in different quadrants. Therefore, it is interesting to design a high-dimensional discrete map with multi-stability [41,42].…”

Exponential Synchronization of Hyperbolic Complex Spatio-Temporal Networks with Multi-Weights

“…A number of important works discuss the synchronization of complex networks [14][15][16][17][18]. This literature shows node dynamics depending only on time.…”