Title: Existence of Noise Induced Order, a Computer Aided Proof,
Abstract: We prove, by a computer aided proof, 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 prove that in this random
dynamical system the increase in amplitude of the noise causes the Lyapunov
exponent to decrease from positive to negative, stabilizing the system. The
method used 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 piecewise differentiable dynamical system on the
interval with additive noise. We also prove that the stationary measure of the
system and its Lyapunov exponent have a Lipschitz stability under several kinds
of perturbation of the noise and of the system itself. The Lipschitz constants
of this stability result are also estimated explicitly.