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Synchronization induced by common colored noise in limit cycle and chaotic systems
Kazuyuki Yoshimura1, Ingrida Valiusaityte, Peter Davis
1NTT Communication Science Laboratories, NTT Corporation, 2-4, Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0237, Japan.
Summary
We investigated how noise correlation affects dynamical system synchronization. Synchronization thresholds differ significantly between limit cycle and chaotic systems, with chaotic systems showing unique dependence on noise correlation decay rates.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Statistical physics
Background:
- Dynamical systems can synchronize when influenced by common external factors.
- Noise with time correlations is a common phenomenon in natural and engineered systems.
- Understanding synchronization mechanisms is crucial for controlling complex behaviors.
Purpose of the Study:
- To analyze the synchronization of dynamical systems driven by exponentially correlated noise.
- To determine the synchronization threshold dependence on noise correlation decay rate.
- To investigate the impact of parameter mismatch on synchronization quality.
Main Methods:
- Mathematical modeling of coupled dynamical systems.
- Analysis of noise with exponential time correlation.
- Derivation and comparison of synchronization conditions for different system types.
- Numerical simulations to verify theoretical predictions.
Main Results:
- Synchronization threshold is independent of correlation decay rate in limit cycle systems.
- In chaotic systems, the threshold diverges for large decay rates and has a minimum at finite rates.
- Parameter mismatch generally degrades synchronization quality.
Conclusions:
- The correlation decay rate of noise plays a critical role in chaotic system synchronization, but not in limit cycle systems.
- Chaotic systems exhibit a more complex response to correlated noise compared to limit cycle systems.
- Parameter mismatch needs careful consideration when designing or analyzing synchronized systems.
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