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Crisis-induced intermittency in two coupled chaotic maps: towards understanding chaotic itinerancy
G Tanaka1, M A F Sanjuán, K Aihara
1Department of Complexity Science and Engineering, Graduate School of Frontier Science, The University of Tokyo, Tokyo, 113-8656, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
Summary
This study reveals how crisis-induced intermittency arises from attractor merging in coupled logistic maps, offering a model for chaotic itinerancy. The findings detail the bifurcation scenario and the role of snap-back repellers in generating these intermittent dynamics.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Intermittency and chaotic itinerancy are key phenomena in nonlinear systems.
- Coupled map lattices provide simplified models for complex dynamics.
- Understanding crisis-induced intermittency is crucial for characterizing chaotic behavior.
Purpose of the Study:
- To elucidate the bifurcation scenario leading to crisis-induced intermittency in a system of two coupled logistic maps.
- To present this system as a fundamental example of chaotic itinerancy.
- To analyze the role of attractor merging and basin structures in generating intermittent dynamics.
Main Methods:
- Analysis of sequential bifurcations leading to chaotic attractors.
- Investigation of basin structures and fractal basin boundary dimensions.
- Numerical simulations to identify crisis events and the generation of snap-back repellers.
Main Results:
- Intermittent dynamics emerge immediately after an attractor-merging crisis of two chaotic attractors.
- Simultaneous contact between attractors and the fractal basin boundary triggers the crisis.
- A snap-back repeller generated during the crisis is responsible for the intermittent transitions.
Conclusions:
- The study clarifies a specific bifurcation scenario for crisis-induced intermittency in coupled logistic maps.
- This system serves as a valuable, simple model for understanding chaotic itinerancy.
- The findings highlight the importance of attractor merging and repeller dynamics in complex systems.