poster: Existence of Noise Induced Order, a Computer Aided Proof

speaker: Stefano Galatolo (Università di Pisa)

abstract: We use 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 $L^1$ 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.

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