Applied & Computational Mathematics seminar: A Dynamical Systems Approach for Most Probable Escape Paths in Non-Gradient Systems

Speaker:  Emmanuel Fleurantin, George Mason University

Title:  A Dynamical Systems Approach for Most Probable Escape Paths in Non-Gradient Systems

Abstract:  Most Probable Escape Paths (MPEPs) have been heavily studied in large deviation theory. Classical methods for computing MPEPs include (but are not limited to) the geometric Minimum Action Method (gMAM) and the p-string method. In this talk, we will focus on heteroclinic orbits of a Hamiltonian system derived from the Friedlin-Wentzell action functional with boundary conditions. We compute the unstable manifold of the equilibrium solution and the stable manifold of a periodic orbit which acts as the boundary of the basin of attraction of our base attractor. The MPEPs are then the transversal intersections of those invariant objects. The Maslov index will help us distinguish local minima of the derived Euler-Lagrange equations from all the heteroclinic solutions in our Hamiltonian system. We will use a 2-dimensional autonomous system with a stable fixed point coexisting with a saddle cycle as a focal point for our methodology.

Time:  Friday, April 8, 2022, 1:30pm-2:30pm

Place:  Zoom