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Phase transition in globally coupled Rössler oscillators
1Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.
Summary
Increasing coupling in identical Rössler oscillators causes a phase transition from disorder to order. This ordered state exhibits partial phase synchronization despite random oscillation amplitudes.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Statistical physics
Background:
- Rössler oscillators are a classic model for chaotic systems.
- Global coupling connects all elements in a network.
- Phase transitions mark significant changes in system behavior.
Purpose of the Study:
- To investigate the phase transition in a globally coupled population of identical Rössler oscillators.
- To characterize the emergent dynamics and synchronization properties.
Main Methods:
- Numerical simulations of coupled Rössler equations.
- Analysis of order-disorder phase transition.
- Application of a self-consistent method for analysis.
Main Results:
- An order-disorder phase transition was observed as the coupling constant increased.
- The ordered phase displayed partial phase synchronization.
- Oscillation amplitudes remained randomly distributed even in the synchronized state.
Conclusions:
- Global coupling can induce order and partial synchronization in chaotic oscillators.
- The system exhibits complex dynamics near the phase transition.
- Self-consistent methods are effective for analyzing such transitions.
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