Stochastic synchronization induced by noise
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916133861326848 |
|---|---|
| author | Song, Yunxiang Witten, Thomas A. |
| author_facet | Song, Yunxiang Witten, Thomas A. |
| contents | Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture. The copies differ only in their arbitrary phases $ϕ$. Weak, randomly-timed external impulses applied to all the copies can synchronize these phases over time. Beyond a threshold strength there is no such convergence to a common phase. Instead, the synchronization becomes erratic: successive impulses produce stochastic fluctuations in the phase distribution $q(ϕ)$, ranging from near-perfect to near-random synchronization. Here we show that the sampled entropies of these phase distributions themselves form a steady-state ensemble, whose average can be made arbitrarily negative by tuning the impulse strength. A random-walk description of the entropy's evolution accounts for the observed exponential distribution of entropies and for the stochastic synchronization phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_13172 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stochastic synchronization induced by noise Song, Yunxiang Witten, Thomas A. Statistical Mechanics Chaotic Dynamics Biological Physics Data Analysis, Statistics and Probability Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture. The copies differ only in their arbitrary phases $ϕ$. Weak, randomly-timed external impulses applied to all the copies can synchronize these phases over time. Beyond a threshold strength there is no such convergence to a common phase. Instead, the synchronization becomes erratic: successive impulses produce stochastic fluctuations in the phase distribution $q(ϕ)$, ranging from near-perfect to near-random synchronization. Here we show that the sampled entropies of these phase distributions themselves form a steady-state ensemble, whose average can be made arbitrarily negative by tuning the impulse strength. A random-walk description of the entropy's evolution accounts for the observed exponential distribution of entropies and for the stochastic synchronization phenomenon. |
| title | Stochastic synchronization induced by noise |
| topic | Statistical Mechanics Chaotic Dynamics Biological Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2108.13172 |