Asymmetric couplings enhance the transition from chimera state to synchronization

Changhai Tian, Hongjie Bi, Xiyun Zhang, Shuguang Guan, and Zonghua Liu
Phys. Rev. E 96, 052209 – Published 14 November 2017

Abstract

Chimera state has been well studied recently, but little attention has been paid to its transition to synchronization. We study this topic here by considering two groups of adaptively coupled Kuramoto oscillators. By searching the final states of different initial conditions, we find that the system can easily show a chimera state with robustness to initial conditions, in contrast to the sensitive dependence of chimera state on initial conditions in previous studies. Further, we show that, in the case of symmetric couplings, the behaviors of the two groups are always complementary to each other, i.e., robustness of chimera state, except a small basin of synchronization. Interestingly, we reveal that the basin of synchronization will be significantly increased when either the coupling of inner groups or that of intergroups are asymmetric. This transition from the attractor of chimera state to the attractor of synchronization is closely related to both the phase delay and the asymmetric degree of coupling strengths, resulting in a diversity of attractor's patterns. A theory based on the Ott-Antonsen ansatz is given to explain the numerical simulations. This finding may be meaningful for the control of competition between two attractors in biological systems, such as the cardiac rhythm and ventricular fibrillation, etc.

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  • Received 4 July 2017
  • Revised 30 October 2017

DOI:https://doi.org/10.1103/PhysRevE.96.052209

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Changhai Tian1,2, Hongjie Bi1, Xiyun Zhang1, Shuguang Guan1, and Zonghua Liu1,*

  • 1Department of Physics, East China Normal University, Shanghai 200062, People's Republic of China
  • 2School of Data Science, Tongren University, Tongren 554300, People's Republic of China

  • *zhliu@phy.ecnu.edu.cn

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Issue

Vol. 96, Iss. 5 — November 2017

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