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Strong persistence of an attractor and generalized partial synchronization in a coupled chaotic system
G Manjunath1, D Fournier-Prunaret
1LATTIS-Institut National des Sciences Appliquées de Toulouse, Université de Toulouse, Toulouse, France. manju.iisc@gmail.com
Chaos (Woodbury, N.Y.)
|July 5, 2011
Summary
Contrary to popular belief, coupling chaotic systems does not always contract phase space. This study demonstrates a counterexample where coupled chaotic systems maintain their original attractor, A × A, and exhibit robust generalized partial synchronization.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Complex systems
Background:
- Coupling discrete time chaotic systems typically leads to phase space contraction.
- This contraction is widely believed to be an inherent property of coupled chaotic dynamics.
Purpose of the Study:
- To challenge the conventional understanding of phase space contraction in coupled chaotic systems.
- To present a counterexample demonstrating the persistence of attractors under nonlinear coupling.
- To investigate the phenomenon of generalized partial synchronization in such systems.
Main Methods:
- Considered two discrete time chaotic systems with an identical attractor, A.
- Developed a nonlinear coupling strategy for these systems.
- Proved robust topological mixing on the product space A × A.
- Analyzed the synchronization properties of the coupled system.
Main Results:
- Demonstrated that nonlinear coupling can preserve the original attractor (A × A) regardless of coupling strength.
- Showcased robust topological mixing on the product attractor A × A.
- Observed robust generalized partial synchronization in the coupled system.
Conclusions:
- The assumption of phase space contraction upon coupling chaotic systems is not universally true.
- Nonlinear coupling can maintain complex dynamics and exhibit robust synchronization phenomena.
- This work opens new avenues for understanding and controlling coupled chaotic systems.
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