Math @ Duke

Publications [#337051] of Yu Cao
Papers Published
 Cao, Y; Lin, L; Zhou, X, Explore stochastic instabilities of periodic points by transition path theory,
Journal of Nonlinear Science, vol. 26 no. 3
(March, 2016),
pp. 755786, Springer Nature [doi]
(last updated on 2019/07/16)
Abstract: © Springer Science+Business Media New York 2016. We consider the noiseinduced transitions from a linearly stable periodic orbit consisting of T periodic points in randomly perturbed discrete logistic map. Traditional large deviation theory and asymptotic analysis at small noise limit cannot distinguish the quantitative difference in noiseinduced stochastic instabilities among the T periodic points. To attack this problem, we generalize the transition path theory to the discretetime continuousspace stochastic process. In our first criterion to quantify the relative instability among T periodic points, we use the distribution of the last passage location related to the transitions from the whole periodic orbit to a prescribed disjoint set. This distribution is related to individual contributions to the transition rate from each periodic points. The second criterion is based on the competency of the transition paths associated with each periodic point. Both criteria utilize the reactive probability current in the transition path theory. Our numerical results for the logistic map reveal the transition mechanism of escaping from the stable periodic orbit and identify which periodic point is more prone to lose stability so as to make successful transitions under random perturbations.


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