English

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 α\alpha-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 Lp(1<p<α)L^{p}(1<p<\alpha) 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.

Keywords

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}
}
R2 v1 2026-06-23T11:54:35.172Z