Calculus of Variations and Geometric Measure Theory

Incontri di Analisi Matematica tra Firenze, Pisa e Siena

The existence of Noise Induced Order, a computer aided proof

Stefano Galatolo

created by paolini on 30 Apr 2019

17 may 2019 -- 14:30   [open in google calendar]

Abstract.

Dynamical systems perturbed by noise appear naturally as models of physical systems. In several interesting cases it can be approached rigorously by computational methods. As a nontrivial example of this, we show a computer aided proof to rigorously show the existence of noise induced order in the model of chaotic chemical reactions where it was first discovered numerically by Matsumoto and Tsuda in 1983. We show that in this random dynamical system the increase of noise causes the Lyapunov exponent to decrease from positive to negative, stabi- lizing the system. The method is based on a certified approximation of the stationary measure in the L1 norm. This is done by an efficient algorithm which is general enough to be adapted to any dynamical system with additive noise on the interval. Time permitting we will also talk about linear response of such systems when the deterministic part of the system is perturbed deterministically.