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This study explores chimera states in coupled oscillators, revealing how initial conditions impact their stability. The basin stability method quantifies the robustness of these complex spatiotemporal patterns.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Chimera states are complex spatiotemporal patterns with coexisting coherent and incoherent dynamics in coupled oscillator networks.
  • Their occurrence, particularly in nonlocally and globally coupled networks, is sensitive to initial conditions, posing a fundamental research challenge.
  • Previous characterizations relied on mean phase velocity and incoherence strength with specific initial conditions.

Purpose of the Study:

  • To investigate the robustness of chimera states, alongside incoherent and coherent states, in relation to varying initial conditions.
  • To apply the basin stability method for quantifying the influence of initial conditions on dynamical states.
  • To analyze nonlocally and globally coupled time-delayed Mackey-Glass oscillators as a model system.

Main Methods:

  • Utilizing the basin stability method, which measures the volume of the basin of attraction.
  • Examining nonlocally and globally coupled time-delayed Mackey-Glass oscillators.
  • Comparing basin stability with previous characterization methods like mean phase velocity and strength of incoherence.

Main Results:

  • The basin stability measure effectively identifies and quantifies the coexistence of different dynamical states (chimera, coherent, incoherent).
  • This method provides insights into the robustness of these states across a broad parameter range.
  • Demonstrates the utility of basin stability beyond specific initial condition preparation.

Conclusions:

  • Basin stability offers a robust quantitative measure for understanding the influence of initial conditions on chimera states and other dynamical regimes.
  • The findings enhance the characterization and prediction of complex dynamics in coupled oscillator systems.
  • This approach facilitates a deeper comprehension of the parameter space supporting diverse collective behaviors.