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Synchronization of nearly identical dynamical systems: Size instability
Suman Acharyya1, R E Amritkar1,2
1Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
Summary
We investigated generalized synchronization stability in coupled dynamical systems. Increasing the central node frequency in star networks enhances synchronization stability, while ring networks show less sensitivity to parameter changes.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- Generalized synchronization is a key phenomenon in coupled dynamical systems.
- Master stability function (MSF) is a powerful tool for analyzing synchronization stability.
- Previous MSF applications were limited for degenerate eigenvalues in coupling matrices.
Purpose of the Study:
- To extend the MSF approach for degenerate eigenvalues in coupling matrices.
- To analyze the size instability in star and ring networks of coupled systems.
- To investigate how network topology and parameters affect synchronization stability.
Main Methods:
- Developed an extended Master Stability Function (MSF) approach.
- Applied MSF to analyze size instability in star and ring network topologies.
- Utilized coupled Rössler systems as a model for numerical verification.
Main Results:
- Demonstrated that increasing the central node frequency in star networks enhances synchronization stability.
- Showed that critical size for instability in star networks can be controlled by frequency.
- Found that critical size in ring networks is largely unaffected by parameter variations.
Conclusions:
- The extended MSF approach is effective for analyzing synchronization in complex networks.
- Network parameters, specifically central node frequency in star networks, can be tuned to improve synchronization stability.
- Ring network synchronization stability is robust against parameter variations.
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