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Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions.

Shiva Dixit1, Sayantan Nag Chowdhury2, Awadhesh Prasad3

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This study explores dynamic interactions in oscillator networks, revealing diverse states like synchronization and amplitude death. Transitions between these states depend on interaction type and initial conditions.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Network science

Background:

  • Oscillator networks exhibit complex behaviors.
  • Understanding dynamic interactions is crucial for predicting network states.
  • Previous studies often focused on simpler coupling mechanisms.

Purpose of the Study:

  • To investigate a novel dynamic coupling in identical oscillator networks.
  • To characterize various asymptotic states, including synchronous, death, mixed, and bistable states.
  • To analyze the nature of dynamical transitions between oscillatory and death states.

Main Methods:

  • Developing a new dynamic coupling design for generic identical oscillators.
  • Employing an average temporal interaction approximation to characterize transitions.
  • Conducting numerical simulations for validation.
  • Examining periodic (Stuart-Landau) and chaotic (Rössler) systems, as well as an ecological model (MacArthur).

Main Results:

  • The new coupling facilitates diverse states: synchronous, amplitude death, oscillation death, mixed, and bistable states.
  • Dynamical transitions are accurately predicted by the average temporal interaction approximation.
  • Phase transition order (first-order vs. second-order) depends on spatial/temporal interaction and initial conditions in the bistable regime.
  • First-order-like transitions are absent in temporal dynamic interactions.

Conclusions:

  • The proposed dynamic coupling offers a versatile mechanism for controlling network states.
  • Initial conditions play a critical role in determining transition dynamics, particularly in bistable regimes.
  • The findings extend to various systems, including chaotic and ecological models, highlighting the broad applicability of the dynamic interaction concept.