05.11.2018 16:15 Stefano Galatolo (UNIPI, Italien):
Perturbations of dynamical systems with additive noise, noise induced order and linear responseMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

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, stabilizing 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.