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Yun Zhu1, Zhigang Zheng2, Junzhong Yang3

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Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Chimera states, a phenomenon of coexisting coherence and incoherence in populations of identical oscillators, have been observed in various physical systems.
  • Understanding the conditions and network structures that support chimera states is crucial for advancing the theory of complex systems.

Purpose of the Study:

  • To investigate the emergence and properties of chimera states in a model of nonlocally coupled identical phase oscillators on complex networks.
  • To determine the influence of network topology (scale-free and Erdös-Rényi) on chimera state formation and stability.
  • To analyze the robustness of chimera states with respect to initial conditions.

Main Methods:

  • Development and analysis of a mathematical model for nonlocally coupled identical phase oscillators.
  • Numerical simulations on scale-free and Erdös-Rényi network topologies.
  • Investigation of system dynamics under varying coupling parameters and initial conditions.

Main Results:

  • The existence of chimera states, characterized by distinct coherent and incoherent oscillator groups, was confirmed.
  • The coherent group within chimera states was found to be invariant to changes in initial conditions.
  • The dependence of chimera state properties on network parameters and topology was systematically explored.

Conclusions:

  • Chimera states are a robust phenomenon in nonlocally coupled oscillator networks, persisting across different network structures.
  • The identified invariant coherent group suggests underlying deterministic mechanisms governing chimera state formation.
  • This study provides a foundational understanding of chimera states in complex networks, with implications for synchronization phenomena.