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Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
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Chimeras on annuli.

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  • 1School of Mathematical and Computational Sciences, Massey University, Private Bag 102-904, North Shore Mail Centre, Auckland, New Zealand.

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This study investigates complex chimera states in coupled oscillator networks using a continuum model. Researchers identified conditions for stable chimera solutions and analyzed their bifurcations.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Chimeras, characterized by coexisting synchronous and asynchronous oscillator groups, appear in coupled oscillator networks.
  • Understanding chimera dynamics is crucial for various fields, including neuroscience and engineering.

Purpose of the Study:

  • To investigate chimera states in networks of nonlocally coupled phase oscillators on an annular domain.
  • To analyze the stability and bifurcations of chimera solutions and rotating waves.

Main Methods:

  • Utilized the Ott/Antonsen ansatz for a continuum-level description of oscillator dynamics.
  • Employed numerical analysis of the order parameter equations.
  • Investigated solutions analogous to multi-headed and spiral wave chimeras.

Main Results:

  • Identified stable chimera solutions on annular domains, dependent on domain width.
  • Characterized rotating waves with different winding numbers, analogous to spiral wave chimeras.
  • Determined parameter ranges for the existence and stability of these solutions, noting subcritical bifurcations.

Conclusions:

  • Chimera states exhibit complex behaviors in annular domains, with stability contingent on domain size.
  • The study provides insights into the formation and stability of chimera patterns in extended systems.
  • Subcritical bifurcations govern the loss of stability for observed chimera and rotating wave solutions.