TY - JOUR
AB - Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the system's first exit from the interior of the unstable orbit occurs typically displays the phenomenon of cycling: The distribution of first-exit locations is translated along the unstable periodic orbit proportionally to the logarithm of the noise intensity as the noise intensity goes to zero. We show that for a large class of such systems, the cycling profile is given, up to a model-dependent change of coordinates, by a universal function given by a periodicized Gumbel distribution. Our techniques combine action-functional or large-deviation results with properties of random Poincare maps described by continuous-space discrete-time Markov chains.
AU - Berglund, Nils
AU - Gentz, Barbara
ID - 2675698
IS - 1
JF - SIAM Journal on Mathematical Analysis
KW - stochastic resonance
KW - cycling
KW - Gumbel distribution
KW - phase slip
KW - synchronization
KW - large deviations
KW - limit cycle
KW - boundary
KW - characteristic
KW - first-exit time
KW - stochastic exit problem
KW - diffusion exit
SN - 0036-1410
TI - ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE
VL - 46
ER -