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Characterizing the phase synchronization transition of chaotic oscillators
Katsuya Ouchi1, Takehiko Horita, Tomoji Yamada
1Kobe Design University, Kobe 651-2196, Japan.
Summary
Researchers studied chaotic phase synchronization transitions and linked them to the zero Lyapunov exponent. They hypothesize this transition involves a switching maximal finite-time zero Lyapunov exponent, confirmed in Rössler systems.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Statistical Physics
Background:
- Phase synchronization is a key phenomenon in coupled chaotic systems.
- Lyapunov exponents characterize the stability and predictability of dynamical systems.
- Understanding transitions in chaotic synchronization is crucial for various applications.
Purpose of the Study:
- To investigate the relationship between chaotic phase synchronization transitions and the zero Lyapunov exponent.
- To propose and test a hypothesis linking these transitions to the switching of the maximal finite-time zero Lyapunov exponent.
- To introduce a novel approach using large deviation analysis for studying synchronization phenomena.
Main Methods:
- Introduction of the maximal finite-time zero Lyapunov exponent within a large deviation analysis framework.
- Investigation using a noisy sine circle map to establish the hypothesis.
- Testing the hypothesis in a unidirectionally coupled Rössler system.
- Utilizing covariant Lyapunov vectors associated with the zero Lyapunov exponent.
Main Results:
- The study establishes a connection between chaotic phase synchronization and the zero Lyapunov exponent.
- Evidence is provided for the hypothesis that transitions involve the switching of the maximal finite-time zero Lyapunov exponent.
- The proposed method is validated in both a model map and a coupled chaotic system.
Conclusions:
- The switching of the maximal finite-time zero Lyapunov exponent is a significant indicator of chaotic phase synchronization transitions.
- The large deviation analysis framework offers a powerful tool for characterizing synchronization phenomena.
- This work contributes to a deeper understanding of complex dynamics in coupled systems.
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