Student Probability Seminar

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Rare transitions in heteroclinic networks

Speaker: Hong-Bin Chen, CIMS

Location: Warren Weaver Hall

Videoconference link: https://nyu.zoom.us/j/98831857610

Date: Thursday, February 17, 2022, 1:30 p.m.

Synopsis:

We consider deterministic dynamics, given by an ODE, perturbed by random white noise with magnitude epsilon, which results in an SDE. We are interested in the dynamics in a network of saddle points connected by their orbits (a heteroclinic network) in 2 dimensions. We will show the probability of dynamics taking a rare transition in the network is polynomial in epsilon. The exponent depends on the contraction-repelling ratio at each saddle along the trajectory. We will show the algorithm to compute the exponent. Then, we explain non rigorously the implication of these results on the hierarchy of meta-stable states in the system on different timescales.