Applied & Computational Mathematics seminar: Identification of tipping points due to bifurcation and noise

Speaker:  Blake Barker, BYU

Title:  Identification of tipping points due to bifurcation and noise

Abstract:  We describe recent results regarding the use of rigorous computation to prove stability properties about traveling waves, and regarding the identification of most probable escape paths in stochastic dynamical systems. Stability bifurcation points indicate regions of parameter space where a small perturbation of parameters leads to solutions near traveling waves with fundamentally different asymptotic behavior. For many systems, the question of stability reduces to determining the spectrum of an ODE eigenvalue problem. We also solve an ODE eigenvalue problem to identify which critical points of the Friedlin-Wentzell functional are minimizers. Minimizers of this functional indicate the most probable noise-induced escape path of a stochastic dynamical system.  We describe recent work using rigorous computation to prove properties about eigenvalue problems of these kinds. 

Time:  Friday, October 5, 2022, 10:30am-11:30am

Place:  Exploratory Hall, Room 4106 or Zoom