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Spatiotemporal dynamics in a ring of N mutually coupled self-sustained systems
H G Enjieu Kadji1, J B Chabi Orou, P Woafo
1Laboratory of Modelling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde, Cameroon. herve@idac.tohoku.ac.jp
Chaos (Woodbury, N.Y.)
|October 2, 2007
Summary
This study analyzes synchronization in coupled oscillators. We identified coupling parameters for full, partial, and no synchronization, and examined how spatial dimensions and parameter mismatches affect stability.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Oscillator networks
Background:
- Coupled oscillators are fundamental to many natural and engineered systems.
- Understanding synchronization phenomena is crucial for predicting system behavior.
- The influence of spatial arrangement and parameter variations on synchronization stability requires further investigation.
Purpose of the Study:
- To analyze the spatiotemporal dynamics of mutually coupled self-sustained oscillators in a ring formation.
- To derive coupling parameters for different synchronization states (full, partial, none) in the absence of parameter mismatches.
- To investigate the impact of spatial dimensions and coupling parameter mismatches on the stability of synchronized states.
Main Methods:
- Analytical derivation of synchronization conditions using variational equations of stability.
- Investigation of the effects of spatial dimensions on stability boundaries.
- Numerical simulations to validate analytical findings and explore parameter mismatch effects.
Main Results:
- Identified specific coupling parameters that lead to full, partial, and no synchronization in a regular ring of oscillators.
- Determined the influence of the spatial dimension of the ring on the stability boundaries of synchronized states.
- Demonstrated that coupling parameter mismatches alter the predicted stability boundaries.
Conclusions:
- The study provides a comprehensive understanding of synchronization dynamics in coupled oscillator rings.
- Analytical and numerical results highlight the critical role of coupling parameters, spatial arrangement, and parameter mismatches in determining synchronization stability.
- The findings offer insights into controlling and predicting the behavior of complex oscillatory systems.
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