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Sharp versus smooth synchronization transition of locally coupled oscillators
M Ciszak1, A Montina, F T Arecchi
1C.N.R.-Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 4, 2008
Summary
Sudden synchronization in coupled oscillators occurs when system response time is less than the refractory period. This condition was verified in neuronal models, including those with noise and chaotic dynamics.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Computational neuroscience
Background:
- Coupled oscillator systems exhibit complex emergent behaviors, including synchronization.
- Understanding the conditions for sudden synchronization is crucial for various scientific fields.
- Previous studies have explored synchronization but a general condition for sudden transitions remains elusive.
Purpose of the Study:
- To establish a general condition for the sudden transition to synchronization in arrays of coupled oscillators.
- To identify the critical relationship between system response time and refractory period for synchronization onset.
- To validate this condition across different models of neuronal dynamics.
Main Methods:
- Theoretical analysis of coupled oscillator arrays with nearest-neighbor interactions.
- Derivation of a general criterion for synchronization onset.
- Numerical simulations and verification using models of excitable systems driven by noise.
- Testing the criterion in models of chaotic oscillators.
Main Results:
- A general condition for sudden synchronization was derived: response time must be less than the refractory period.
- This criterion was successfully verified in both noise-driven excitable neuronal models and chaotic oscillator models.
- The findings highlight the critical role of the interplay between response and recovery dynamics.
Conclusions:
- The derived condition provides a fundamental insight into the mechanisms of sudden synchronization in coupled systems.
- This criterion is broadly applicable to various oscillator networks, particularly in neuroscience.
- The results advance the understanding of emergent collective behaviors in complex systems.
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