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The smallest chimera state for coupled pendula.

Jerzy Wojewoda1, Krzysztof Czolczynski1, Yuri Maistrenko1,2,3

  • 1Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland.

Scientific Reports
|October 8, 2016
PubMed
Summary

Researchers discovered the smallest chimera state in a system of three coupled chaotic pendula. This finding demonstrates that complex chimera states, with both synchronized and incoherent behaviors, can occur in small, simple mechanical oscillator networks.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Network science

Background:

  • Chimera states are spatiotemporal patterns observed in coupled oscillator systems.
  • These states involve coexisting synchronous and incoherent behaviors among oscillators.
  • Typically found in large ensembles, their occurrence in small systems is a recent area of investigation.

Purpose of the Study:

  • To investigate the possibility of chimera states in small networks of coupled oscillators.
  • To identify and characterize the smallest possible chimera state.
  • To demonstrate the experimental observability of such states in simple mechanical systems.

Main Methods:

  • Analysis of three coupled chaotic pendula.
  • Derivation of elementary dynamical equations from Newton's laws.
  • Identification of a chimera state pattern with two synchronized and one incoherent oscillator.

Main Results:

  • The smallest chimera state was identified in a system of three coupled chaotic pendula.
  • This state is characterized by the coexistence of two synchronized and one incoherent oscillator.
  • The chimera state was shown to be observable in simple mechanical experiments.

Conclusions:

  • Chimera states can occur in systems with a small number of coupled oscillators.
  • The smallest chimera state provides a simplified model for studying these complex phenomena.
  • Findings suggest the relevance of chimera states in small networks for various real-world applications.