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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Investigating synchronization phenomena in coupled chaotic oscillators is crucial for understanding emergent behaviors in complex systems.
  • Star network topology, with a central hub and peripheral nodes, presents unique dynamics for emergent behavior studies.
  • Invariant symmetry in oscillators and timescale variations are key factors influencing transition dynamics.

Purpose of the Study:

  • To analyze the transition to synchronization in a chaotic oscillator ensemble on a star network.
  • To explore emergent behaviors under symmetry-preserving and symmetry-breaking coupling conditions.
  • To understand the role of timescale variations in driving explosive transitions.

Main Methods:

  • Utilizing master stability functions for analyzing stability and synchronization thresholds.
  • Employing Lyapunov exponents to quantify chaotic dynamics and synchronization.
  • Performing detailed stability analysis to identify transition points and hysteresis.

Main Results:

  • Symmetry-preserving coupling leads to consecutive explosive synchronization and death transitions with hysteresis.
  • Intermediate clusters and intermittent synchrony (antisynchrony) emerge due to driving-induced multistability.
  • Symmetry-breaking coupling results in a direct explosive death transition from an oscillatory state.

Conclusions:

  • The study demonstrates distinct explosive transition pathways in chaotic oscillator networks based on symmetry.
  • Network topology and coupling properties significantly influence synchronization and death phenomena.
  • Timescale variations can induce complex emergent behaviors like multistability and intermittent synchrony.