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An analytic criterion for generalized synchronization in unidirectionally coupled systems based on the auxiliary
1Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Hong Kong. tcwongca@inet.polyu.edu.hk
Chaos (Woodbury, N.Y.)
|October 2, 2012
Summary
We developed an analytic criterion to study generalized synchronization (GS) in coupled systems. More equilibria increase the chance of GS but may hinder strong GS occurrence.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Generalized synchronization (GS) is a phenomenon in coupled dynamical systems where one system's dynamics are constrained by another.
- Investigating GS is crucial for understanding information transfer and control in complex systems.
- Existing methods for detecting GS, like Lyapunov exponents, can be computationally intensive.
Purpose of the Study:
- To develop a novel analytic criterion for detecting generalized synchronization in unidirectionally coupled systems.
- To provide an alternative and potentially more efficient method for analyzing GS.
- To explore the relationship between system equilibria and the occurrence of generalized synchronization.
Main Methods:
- The auxiliary system approach was employed to transform the GS existence problem.
- The problem was reformulated as an eigenvalue problem for analysis.
- Numerical simulations were conducted to validate the criterion.
Main Results:
- The developed analytic criterion accurately estimates the occurrence of generalized synchronization.
- The criterion's accuracy is comparable to the response Lyapunov exponents method.
- The criterion may estimate the threshold for strong generalized synchronization.
- A higher number of equilibria in coupled systems increases the likelihood of GS.
Conclusions:
- The analytic criterion offers a reliable method for investigating generalized synchronization.
- The number of equilibria significantly influences the conditions for generalized synchronization.
- Further research can explore the criterion's application to different types of coupled systems and synchronization phenomena.
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