Title： Explore stochastic instabilities of periodic points by transition path theory

Speaker：Prof. Xiang Zhou（City University of Hong Kong）

Time：19:30-20:30 P.M.Oct 16th, 2015

Location：Room 4318, Building No.4, Wushan Campus

Abstract:We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable period orbit consisting of $T$ periodic points. We generalize the transition path theory to the discrete-time continuous-spacestochastic process to attack this problem. As a first criterion of quantifying the relative instability among $T$ periodic points,we compare the distribution of the last passage locations in the transitions from the whole periodic orbit to a prescribed set far away.The second criterion is based on the capacity of the transition paths associated with each periodic point.Both criteria utilise 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 transitionsunder random perturbations.

Introduction to the speaker: Dr Xiang Zhou received his BSc from Peking University and PhD from Princeton University. Before joining City University in 2012, he worked as a research associate at Princeton University and Brown University. His major research interests include noise-induced transitions and stochastic systems, the study of rare events and its applications in physics, chemistry, biology, engineering and finance.