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Self-adaptation of chimera states

Nan Yao, Zi-Gang Huang, Hai-Peng Ren, Celso Grebogi, and Ying-Cheng Lai
Phys. Rev. E 99, 010201(R) – Published 9 January 2019

Abstract

Chimera states in spatiotemporal dynamical systems have been investigated in physical, chemical, and biological systems, and have been shown to be robust against random perturbations. How do chimera states achieve their robustness? We uncover a self-adaptation behavior by which, upon a spatially localized perturbation, the coherent component of the chimera state spontaneously drifts to an optimal location as far away from the perturbation as possible, exposing only its incoherent component to the perturbation to minimize the disturbance. A systematic numerical analysis of the evolution of the spatiotemporal pattern of the chimera state towards the optimal stable state reveals an exponential relaxation process independent of the spatial location of the perturbation, implying that its effects can be modeled as restoring and damping forces in a mechanical system and enabling the articulation of a phenomenological model. Not only is the model able to reproduce the numerical results, it can also predict the trajectory of drifting. Our finding is striking as it reveals that, inherently, chimera states possess a kind of “intelligence” in achieving robustness through self-adaptation. The behavior can be exploited for the controlled generation of chimera states with their coherent component placed in any desired spatial region of the system.

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  • Received 24 October 2018

DOI:https://doi.org/10.1103/PhysRevE.99.010201

©2019 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

Nan Yao1, Zi-Gang Huang2,*, Hai-Peng Ren3, Celso Grebogi4, and Ying-Cheng Lai5,6

  • 1Department of Applied Physics, Xi'an University of Technology, Xi'an 710048, China
  • 2The Key Laboratory of Biomedical Information Engineering of Ministry of Education, National Engineering Research Center of Health Care and Medical Devices, The Key Laboratory of Neuro-informatics & Rehabilitation Engineering of Ministry of Civil Affairs, and Institute of Health and Rehabilitation Science, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an 710049, China
  • 3Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi'an University of Technology, Xi'an 710048, China
  • 4Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
  • 5School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
  • 6Department of Physics, Arizona State University, Tempe, Arizona 85287, USA

  • *huangzg@xjtu.edu.cn

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Issue

Vol. 99, Iss. 1 — January 2019

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