具有可加白噪音的耦合系统的同步

在单边Lipschitz耗散条件下,考虑具有可加白噪音的耦合系统的两种同步现象,即不同解之间的同步和同一个解的不同分量之间的同步.首先证明了该耦合系统存在单点集随机吸引子,从而发生不同解之间的同步现象,此外该随机吸引子还是系统的唯一平稳解.然后证明了当耦合系数趋于无穷大时,该系统解的每一个分量在有限时间区间内一致地趋于平均系统的平稳解.

Synchronization of coupled systems with additive noise

This paper is devoted to two kinds of synchronization of solutions (i. e. , between any two solutions and among components of solutions) of the N-coupled Ito stochastic differential equations (SDEs) with additive noises under the one-sided dissipative Lipschitz conditions. We first show that the random dynamical system generated by the coupled SDEs has a singleton sets random attractor which implies the synchronization of any two solutions. Moreover, the singleton sets random attractor is a stationary solution of the coupled SDEs. Then, we show that any components of the solutions of coupled SDEs converge to the stationary solution of the averaged SDE uniformly on any finite time in-terval as the coupled coefficient tends to infinity. Our results generalize the work on two Ito SDEs in 3].