Explore Stochastic Instabilities of Periodic Points by Transition Path Theory
主 题: Explore Stochastic Instabilities of Periodic Points by Transition Path Theory
报告人: Prof. Xiang Zhou (City University of Hong Kong)
时 间: 2015-06-03 16:00-17:00
地 点: 理科一号楼1493室
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-space stochastic 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 transitions under random perturbations.