Abstract
We develop and validate an algorithm for integrating stochastic differential equations under green noise. Utilizing it and the standard methods for computing dynamical systems under red and white noise, we address the problem of synchronization among chaotic oscillators in the presence of common colored noise. We find that colored noise can induce synchronization, but the onset of synchronization, as characterized by the value of the critical noise amplitude above which synchronization occurs, can be different for noise of different colors. A formula relating the critical noise amplitudes among red, green, and white noise is uncovered, which holds for both complete and phase synchronization. The formula suggests practical strategies for controlling the degree of synchronization by noise, e.g., utilizing noise filters to suppress synchronization.
| Original language | English |
|---|---|
| Article number | 056210 |
| Number of pages | 8 |
| Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |
| Volume | 79 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - May 2009 |
Keywords
- chaos
- differential equations
- nonlinear dynamical systems
- oscillations
- stochastic processes
- synchronisation
- white noise
- runge-kutta algorithms
- green noise
- stochastic resonance
- coherence resonance
- external noise
- oscillators
- transitions