The persistence of synchronization under $\alpha$-stable noise

Yanjie Zhang; Li Lin; Jinqiao Duan; Hongbo Fu

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arXiv · 1910.11546

The persistence of synchronization under $\alpha$-stable noise

Yanjie Zhang·Li Lin·Jinqiao Duan·Hongbo Fu

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Abstract

This work is about the synchronization of nonlinear coupled dynamical systems driven by $\alpha$-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 $L^{p}(1<p<\alpha)$ 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.

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Yanjie Zhang, Li Lin, Jinqiao Duan, Hongbo Fu. 2019-10-25. The persistence of synchronization under $\alpha$-stable noise. https://arxiv.org/abs/1910.11546

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