Dynamics and Synchronization of Complex-Valued Ring Networks

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Article number2230011
Journal / PublicationInternational Journal of Bifurcation and Chaos
Volume32
Issue number5
Publication statusPublished - Apr 2022

Abstract

Networks of coupled oscillators have been used to model various real-world self-organizing systems. However, the dynamics, especially chaos and bifurcation, of complex-valued networks are rarely investigated. In this paper, a ring network of interacting complex-valued van der Pol oscillators is studied to model the formation of ring dynamics. Although there are only stable limit cycles in a complex-valued van der Pol oscillator, chaos, hyperchaos, and coexisting chaotic attractors are observed from the ring network, which are analyzed by using the Lyapunov exponent spectrum, bifurcation diagram and 0-1 test. In addition, complexity analysis on nonlinear coefficients and coupling strengths illustrates that the range of parameters within the chaotic (hyperchaotic) region has positive correlation with the number of oscillators. It is shown that the chaotic bifurcation path is highly robust against the size variation of the ring network, which always evolves to chaos directly from period-1 and quasi-periodic states, respectively. Moreover, it is demonstrated that complete synchronization and phase synchronization of oscillations are stable in a large-scale ring network, while chaotic phase synchronization is unstable in a small-scale network.

Research Area(s)

  • Ring network, chaotic phase synchronization, complex-valued van der Pol oscillator, PROJECTIVE SYNCHRONIZATION, CHAOTIC SYSTEMS, REAL, VAN

Citation Format(s)

Dynamics and Synchronization of Complex-Valued Ring Networks. / Zhao, Xiu; Liu, Jian; Chen, Guanrong; Chai, Lin; Wang, Dan.

In: International Journal of Bifurcation and Chaos, Vol. 32, No. 5, 2230011, 04.2022.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review