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Riddling: Chimera's dilemma.

V Santos1, J D Szezech1, A M Batista1

  • 1Graduate in Science Program, State University of Ponta Grossa, Ponta Grossa, Paraná 84030-900, Brazil.

Chaos (Woodbury, N.Y.)
|September 6, 2018
PubMed
Summary

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This summary is machine-generated.

Chimera states in Hénon maps arise from coexisting basins of attraction, causing hysteresis. Their sensitivity to initial conditions depends on fractal basin boundaries, presenting a

Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Coexisting basins of attraction in dynamical systems can lead to hysteretic behavior.
  • Chimera states, characterized by simultaneous coherent and incoherent domains, emerge from such coexisting basins.

Purpose of the Study:

  • To investigate basin of attraction properties and boundaries for chimera states in a circulant network of Hénon maps.
  • To characterize the sensitivity of chimera state density to parameter changes and initial conditions.

Main Methods:

  • Analysis of basin of attraction properties in a circulant network of Hénon maps.
  • Characterization of basin boundaries using the uncertainty exponent.
  • Investigation of state density variations with parameter changes and initial condition perturbations.

Related Experiment Videos

Main Results:

  • Chimera states emerge due to coexisting basins of attraction, leading to invariant or subtly changing state distributions.
  • Basin boundaries between coherent, incoherent, and chimera states exhibit fractal and riddled characteristics.
  • The density of chimera states demonstrates moderate to high sensitivity to initial conditions.

Conclusions:

  • The coexistence of basins of attraction is crucial for the emergence and behavior of chimera states.
  • Fractal and riddled basin boundaries are responsible for the observed sensitivity of chimera states to initial conditions.
  • This sensitivity, termed the 'chimera's dilemma,' highlights the complex dynamics within these networks.