The persistence of synchronization under $\alpha$-stable noise
Probability
2019-10-28 v1
Abstract
This work is about the synchronization of nonlinear coupled dynamical systems driven by -stable noise. Firstly, we provide a novel technique to construct the relationship between synchronized system and slow-fast system. Secondly, we show that the slow component of original systems converges to the mild solution of the averaging equation under sense. Finally, using the results of averaging principle for stochastic dynamical system with two-time scales, we show that the synchronization effect is persisted provided equilibria are replaced by stationary random solutions.
Cite
@article{arxiv.1910.11546,
title = {The persistence of synchronization under $\alpha$-stable noise},
author = {Yanjie Zhang and Li Lin and Jinqiao Duan and Hongbo Fu},
journal= {arXiv preprint arXiv:1910.11546},
year = {2019}
}