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Alexey A Koronovskii1, Olga I Moskalenko1, Anatoliy A Pivovarov1

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Researchers studied the transition to generalized synchronization in chaotic oscillators. They found this transition is an on-off intermittency, similar to unidirectional systems, using a local Lyapunov exponent method.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Coupled chaotic oscillators exhibit complex behaviors, including synchronization.
  • Distinguishing between asynchronous and synchronous states is crucial for understanding system dynamics.
  • Generalized synchronization is a complex phenomenon observed in coupled chaotic systems.

Purpose of the Study:

  • To investigate the transition from asynchronous behavior to generalized synchronization in mutually coupled chaotic oscillators.
  • To develop and validate a method for identifying epochs of synchronous and asynchronous motion in time series data.
  • To determine the nature of the transition to generalized synchronization in these systems.

Main Methods:

  • Utilized time series analysis of mutually coupled chaotic oscillators.
  • Employed a novel method based on the calculation of local Lyapunov exponents.
  • Validated the method using unidirectionally coupled dynamical systems with known transition types.

Main Results:

  • Successfully separated synchronous and asynchronous motion epochs in time series.
  • Demonstrated that the transition to generalized synchronization in mutually coupled systems is an on-off intermittency.
  • Confirmed the universality of this transition type by comparing with unidirectionally coupled systems.

Conclusions:

  • The proposed local Lyapunov exponent method is effective for analyzing transitions in coupled chaotic systems.
  • The transition to generalized synchronization in mutually coupled chaotic oscillators is characterized by on-off intermittency.
  • This finding provides a deeper understanding of synchronization dynamics in complex systems.