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Generalized synchronization of chaos in autonomous systems
O Alvarez-Llamoza1, M G Cosenza
1Departamento de Física, FACYT, Universidad de Carabobo, Valencia, Venezuela.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2008
Summary
Researchers extend generalized synchronization of chaos to autonomous spatiotemporal systems. This phenomenon allows chaotic states within a system to synchronize without relying on external coupling functions.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Spatiotemporal Systems
Background:
- Generalized synchronization of chaos is a known phenomenon in driven dynamical systems.
- Autonomous spatiotemporal systems present unique challenges for synchronization studies.
Purpose of the Study:
- To extend the concept of generalized synchronization of chaos to autonomous spatiotemporal systems.
- To investigate the conditions under which generalized synchronization emerges in these systems.
Main Methods:
- An analogy is drawn between driven response maps with probabilistic external drives and autonomous coupled map systems with global interactions.
- The stability conditions for generalized synchronized states are analyzed in both system types.
Main Results:
- The study demonstrates that generalized synchronization can occur in autonomous spatiotemporal systems.
- Conditions for the stability of generalized synchronized states are found to be equivalent in driven and autonomous systems under certain circumstances.
- Similar minimal conditions for the emergence of generalized synchronization are identified in both contexts.
Conclusions:
- Generalized synchronization of chaos is achievable in autonomous spatiotemporal systems.
- The findings reveal a fundamental similarity in the emergence conditions for generalized synchronization across different types of dynamical systems.
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