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Plasticity and learning in a network of coupled phase oscillators
Philip Seliger1, Stephen C Young, Lev S Tsimring
1Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA.
Summary
This study explores a generalized Kuramoto model, revealing that synchronized oscillator clusters can form and store information. These stable, robust clusters adapt their coupling strength based on phase differences.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- The Kuramoto model is a fundamental framework for studying synchronization in coupled oscillator systems.
- Understanding how coupling dynamics influence emergent collective behavior is crucial in complex systems.
- Adaptive coupling mechanisms are essential for creating robust and controllable synchronized states.
Purpose of the Study:
- To investigate a generalized Kuramoto model with adaptive coupling strengths.
- To explore the formation and stability of synchronized clusters.
- To assess the potential for information storage and retrieval using phase differences within clusters.
Main Methods:
- Studied a generalized Kuramoto model with a slow-varying coupling matrix.
- Coupling dynamics were driven by oscillator phase differences, strengthening for synchronization and weakening otherwise.
- Analyzed the emergence of stable synchronized clusters under external driving and noise.
Main Results:
- Identified a family of stable solutions corresponding to synchronized clusters of varying sizes.
- Demonstrated that external driving can initiate specific synchronized clusters.
- Showcased the robustness of synchronized states against noise and frequency variations.
Conclusions:
- The generalized Kuramoto model supports stable, adaptable synchronized clusters.
- These clusters exhibit properties suitable for information storage and retrieval.
- The adaptive coupling mechanism provides a pathway for controlling and utilizing collective dynamics.