Limits to detection of generalized synchronization in delay-coupled chaotic oscillators
Hideyuki Kato1, Miguel C Soriano2, Ernesto Pereda3
1Center for Simulation Sciences, Ochanomizu University, 2-1-1 Ohtsuka Bunkyo-ku, 112-8610 Tokyo, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
Summary
Detecting generalized synchronization in coupled chaotic oscillators is challenging. Direct time-series analysis methods often fail to reliably identify synchronization, even in identical systems connected through intermediate oscillators.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Generalized synchronization is a key phenomenon in coupled chaotic oscillators.
- The auxiliary system approach verifies generalized synchronization but has practical limitations.
- Direct time-series analysis methods are sought for practical detection.
Purpose of the Study:
- To evaluate the reliability of direct time-series analysis for detecting generalized synchronization.
- To compare common synchronization indices against the auxiliary system approach.
- To investigate challenges in detecting generalized synchronization in unidirectionally coupled chaotic oscillators.
Main Methods:
- Analysis of delay-coupled chaotic oscillators in unidirectional ring configurations.
- Complementary use of the auxiliary system approach and direct time-series analysis indices.
- Quantification of generalized and phase synchronization from noise-free time series.
Main Results:
- Direct synchronization indices did not consistently match the auxiliary system approach results.
- Detecting generalized synchronization is challenging in systems with intermediate oscillators.
- Identical oscillators connected via a chain exhibit synchronization detection difficulties.
Conclusions:
- Direct time-series analysis methods are not always reliable for detecting generalized synchronization.
- The indirect nature of coupling through multiple oscillators complicates synchronization detection.
- Findings impact the interpretation of coupled system dynamics and applications.
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