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Mechanism for the riddling transition in coupled chaotic systems
1Department of Physics, Kangwon National University, Chunchon, Kangwon-Do 200-701, Korea. sykim@cc.kangwon.ac.kr
Summary
We found a new way chaos synchronization is lost in asymmetric systems. A transcritical contact bifurcation causes global riddling, leading to unpredictable behavior and power-law scaling.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Chaos synchronization is crucial in many fields.
- Understanding synchronization loss is key to controlling complex systems.
- Asymmetric coupled chaotic systems exhibit unique dynamics.
Purpose of the Study:
- Investigate the loss of chaos synchronization in coupled chaotic systems without symmetry.
- Identify the bifurcation mechanisms responsible for synchronization loss.
- Characterize the resulting riddled basins of attraction.
Main Methods:
- Analysis of bifurcations of unstable periodic orbits.
- Examination of the synchronous chaotic attractor (SCA).
- Study of basin boundary properties and scaling laws.
Main Results:
- A novel mechanism for direct transition to global riddling via transcritical contact bifurcation.
- This mechanism differs from that in symmetric systems.
- Riddled basins exhibit repelling tongues, leading to divergent orbits and power-law scaling.
Conclusions:
- The identified bifurcation mechanism provides new insights into synchronization loss in asymmetric systems.
- The characterization of riddled basins with divergence and uncertainty exponents is significant.
- Findings contribute to the understanding of complex dynamics and predictability in chaotic systems.
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