CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

8 septembre 2020 de 10 h 00 à 11 h 00 (heure de Montréal/HNE) Réunion Zoom

A proof of Noise Induced Order in the BZ map, and some remarks on the phenomenon

Séminaire par Isaia Nisoli (Universidade Federal do Rio de Janeiro, Brazil)

In this talk I will present a Computer Aided Proof of Noise Induced Order (NIO) in a model associated with the Belousov-Zhabotinsky reaction: when studying the random dynamical system with additive noise associated to the BZ map, as the noise amplitude increases the Lyapunov exponent of the model transitions from positive to negative. The proof is obtained through rigorous approximation of the stationary measure using Ulam method.

I will also show a sufficient condition for the existence of NIO in a wide family of one-dimensional examples.

[1] S. Galatolo, M. Monge, I. Nisoli "Existence of Noise Induced Order: a computer aided proof", Nonlinearity 33(9)
[2] I. Nisoli "Sufficient Conditions for Noise Induced Order in 1-dimensional systems", arXiv:2003.08422