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Emergent dynamics in delayed attractive-repulsively coupled networks.

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This study explores how networks of identical oscillators transition between oscillation, amplitude death, and oscillation death states. We identified three distinct transition scenarios and analyzed the impact of time delays on these dynamics.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Coupled oscillator networks exhibit complex emergent behaviors.
  • Time delays and localized interactions significantly influence network dynamics.
  • Understanding transitions between oscillatory and non-oscillatory states is crucial in various scientific fields.

Purpose of the Study:

  • To investigate emergent dynamics like oscillation quenching and revival in globally coupled identical oscillators.
  • To identify and characterize transition phenomena between oscillatory state (OS), amplitude death (AD), and oscillation death (OD) states.
  • To analyze the role of symmetry-breaking localized repulsive delayed interactions and time delays.

Main Methods:

  • Systematic parameter space exploration of coupled Stuart-Landau and Rössler systems.
  • Derivation of a reduced low-dimensional model based on observed clustering behavior.
  • Analysis of bifurcation transitions in both the full network and the reduced model.

Main Results:

  • Identified three transition scenarios: OS-AD-OD, OS-AD-OS, and OS-OD.
  • Demarcated OS, AD, and OD regimes in the parameter space, influenced by time delays.
  • Demonstrated satisfactory agreement between the reduced model and the full network dynamics.

Conclusions:

  • Localized repulsive delayed interactions can induce diverse emergent dynamics in coupled oscillator networks.
  • Time delay plays a critical role in governing the transitions between different dynamical states.
  • The developed reduced model effectively captures the essential dynamics of the large network, facilitating further analysis.