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Exact explosive synchronization transitions in Kuramoto oscillators with time-delayed coupling.

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This study explores explosive synchronization in coupled oscillators. Time delays impact transitions when coupling strength increases but not when it decreases, offering insights into real-world systems.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Theoretical Physics

Background:

  • Synchronization is prevalent in natural and engineered systems like neural networks and power grids.
  • Transitions into or out of synchrony are influenced by factors including frequency, coupling, time delays, and network structure.
  • Explosive synchronization, characterized by abrupt transitions, is a key phenomenon in coupled oscillator systems.

Purpose of the Study:

  • To investigate the stability of incoherent and coherent states in a generalized Kuramoto model.
  • To analyze transitions to and from explosive phase synchronization in systems with time-delayed coupling.
  • To determine the precise effect of time delays on critical coupling strengths for synchronization transitions.

Main Methods:

  • Utilized a generalized Kuramoto model for time-delay coupled phase oscillators.
  • Incorporated frequency-weighted coupling to model interactions.
  • Analytically derived exact formulas for critical coupling strengths at various time delays for both forward and backward transitions.

Main Results:

  • Time delay was found to not influence the backward transition (decreasing coupling strength).
  • Time delay can alter the critical coupling strength for the forward transition (increasing coupling strength).
  • Exact analytical formulas for critical coupling strengths were derived for different time delays.

Conclusions:

  • Time delays play a crucial role in the dynamics of explosive synchronization, particularly during transitions driven by increasing coupling.
  • The findings offer significant insights into the mechanisms underlying explosive synchronization in systems with inherent time delays.
  • This research contributes to understanding synchronization phenomena in diverse physical and biological systems where time delays are common.