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Synchronization by noise for traveling pulses

  • Joris van Winden (TU Delft)
E2 10 (Leon-Lichtenstein)

Abstract

We consider synchronization by noise for stochastic partial differential equations which support traveling pulse solutions, such as the FitzHugh-Nagumo equation. We show that any two pulse-like solutions which start from different positions but are forced by the same realization of a multiplicative noise, converge to each other in probability on a time scale proportional to the inverse square of the noise amplitude. The noise is assumed to be Gaussian, white in time, colored and periodic in space, and non-degenerate only in the lowest Fourier mode.

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