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This summary is machine-generated.

We extended the Kuramoto-Sakaguchi model to second-order phase approximation for coupled nonidentical Stuart-Landau oscillators. This enhanced model accurately captures chimera states, unlike simpler models.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • The Kuramoto-Sakaguchi model is a standard for studying coupled oscillators.
  • Higher-order approximations are needed for complex network dynamics.
  • Chimera states in nonlocally coupled oscillators are a current research focus.

Purpose of the Study:

  • To extend the Kuramoto-Sakaguchi model to second-order phase approximation.
  • To analyze the dynamics of nonidentical Stuart-Landau oscillators in networks.
  • To investigate the emergence and characteristics of chimera states.

Main Methods:

  • Derivation of a second-order phase approximation for coupled oscillators.
  • Analysis of an ensemble of nonidentical Stuart-Landau oscillators.
  • Application to nonlocally coupled systems exhibiting chimera states.

Main Results:

  • The coupling matrix directly translates into the phase equation coupling structure.
  • The second-order phase model reproduces chimera shape dependence on coupling strength.
  • First-order models fail to capture this dependence, highlighting the importance of high-order reduction.

Conclusions:

  • The derived second-order phase model offers a more accurate description of complex oscillatory networks.
  • This work establishes a link between network coupling matrices and multibody interactions in phase models.
  • The findings advance the understanding of chimera states and network dynamics.