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Extreme events emerge in coupled Rössler oscillators due to in-phase synchronization and on-off intermittency. These phenomena drive chaotic dynamics, impacting average velocity, synchronization error, and transverse variables, as analyzed by extreme value theory.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • The Rössler system, a minimal-dimensional model for chaos, is widely studied.
  • Understanding extreme events in coupled chaotic oscillators is crucial for complex system dynamics.

Purpose of the Study:

  • Investigate the emergence and mechanisms of extreme events in diffusively coupled Rössler oscillators.
  • Analyze the role of synchronization and intermittency in generating these events.

Main Methods:

  • Numerical simulation of two bidirectionally coupled Rössler oscillators.
  • Application of generalized extreme value theory to analyze extreme event statistics.
  • Examination of average velocity, synchronization error, and transverse variables.

Main Results:

  • Extreme events observed in average velocity, synchronization error, and transverse variables.
  • In-phase synchronization triggers extreme events in average velocity.
  • On-off intermittency drives extreme events in synchronization error and transverse dynamics, including bubble transitions.

Conclusions:

  • Coupling strength and frequency mismatch significantly influence extreme event genesis.
  • Generalized extreme value theory and exponential inter-event intervals characterize extreme events in average velocity.
  • On-off intermittency is a key mechanism for extreme event generation in coupled chaotic systems.