Small noise and long time phase diffusion in stochastic limit cycle oscillators
نویسندگان
چکیده
We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is performed in the limit of small noise – that is, we modulate the noise by a factor ε ց 0 – and on a long time horizon. We prove explicit estimates on the proximity of the noisy trajectory and the limit cycle up to times exp (
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