Synchronization of Systems with Multiplicative Noise

Description

The synchronization of Stratonovich stochastic di erential equations (SDE) with a one-sided dissipative Lipschitz drift and linear multiplicative noise is investigated by transforming the SDE to random ordinary di erential equations (RODE) and synchronizing their dynamics. In terms of the original SDE this gives synchronization only when the driving noises are the same. Otherwise, the synchronization is modulo exponential factors involving Ornstein-Uhlenbeck processes corresponding to the driving noises. Moreover, this occurs no matter how large the intensity coe cients of the noise.

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