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Nonlinearity of local dynamics promotes multi-chimeras.

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The nonlinearity of coupled oscillators significantly impacts complex chimera states. Stronger nonlinearity in Van der Pol oscillators leads to multi-chimera states and alters their stability and dynamics, with time delay also influencing patterns.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Chimera states are spatio-temporal patterns exhibiting coexisting synchronous and asynchronous dynamics in coupled oscillator systems.
  • Understanding the influence of individual element characteristics on chimera states is crucial for complex systems research.

Purpose of the Study:

  • To investigate how the nonlinearity of individual oscillators affects the emergence and properties of chimera states.
  • To explore the impact of varying nonlinearity in Van der Pol oscillators on multi-chimera states and their stability.
  • To analyze the influence of time delay on chimera patterns.

Main Methods:

  • Utilized networks of nonlocally coupled Van der Pol oscillators.
  • Varied the bifurcation parameter of the Van der Pol system to control nonlinearity from sinusoidal to relaxation oscillations.
  • Analyzed stability regimes and mean phase velocity profiles of oscillators.
  • Investigated the effect of time delay on chimera patterns.

Main Results:

  • Increased nonlinearity in Van der Pol oscillators promotes the formation of multi-chimera states with multiple incoherent domains.
  • Significant changes in the stability regimes of multi-chimera states were observed with increasing nonlinearity.
  • Mean phase velocity profiles of oscillators were found to change considerably as nonlinearity intensified.
  • Time delay was demonstrated to influence the characteristics of chimera patterns.

Conclusions:

  • The nonlinearity of individual elements is a key factor in shaping chimera states, particularly inducing multi-chimera states.
  • The stability and dynamics of chimera states are sensitive to the degree of nonlinearity and the presence of time delays.
  • This study provides insights into the fundamental mechanisms governing complex spatio-temporal patterns in coupled nonlinear systems.