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Chaotic itinerancy generated by coupling of Milnor attractors
Ichiro Tsuda1, Toshiya Umemura
1Department of Mathematics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan.
Chaos (Woodbury, N.Y.)
|August 30, 2003
Summary
We found chaotic itinerancy in coupled Milnor attractors, characterized by attractor ruins and slow Lyapunov exponent convergence. Large fluctuations in the largest Lyapunov exponent suggest this phenomenon.
Area of Science:
- Dynamical Systems
- Chaos Theory
- Nonlinear Dynamics
Background:
- Milnor attractors are fundamental objects in dynamical systems.
- Understanding chaotic behavior and its characterization is crucial.
- Coupled systems can exhibit complex dynamics not present in isolated ones.
Purpose of the Study:
- To report the existence of chaotic itinerancy in a coupled Milnor attractor system.
- To characterize the nature of attractor ruins in this system.
- To identify new indicators of chaotic itinerancy.
Main Methods:
- Analysis of coupled Milnor attractor systems.
- Investigation of attractor ruins (tori or local chaos).
- Calculation and analysis of Lyapunov exponents, including their convergence and fluctuations.
Main Results:
- Chaotic itinerancy was confirmed in the coupled Milnor attractor system.
- Attractor ruins were observed as tori or local chaos.
- Slow convergence of Lyapunov exponents indicates nonstationary behavior for single orbits.
- Slow decay of large fluctuations in the largest Lyapunov exponent is proposed as a new indicator.
Conclusions:
- Chaotic itinerancy is a feature of coupled Milnor attractor systems.
- The behavior of single orbits can appear nonstationary due to slow convergence.
- The decay rate of large Lyapunov exponent fluctuations offers a novel signature for chaotic itinerancy.