Existence of multiple noise-induced transitions in a Lasota-Mackey map

We prove the existence of multiple noise-induced transitions in the Lasota-Mackey mapl, which is a class of one-dimensional random dynamical system with additive noise. The result is achieved by rigorous computer assisted estimates. We first approximate the stationary distribution of the random dynamical system and then compute certifiederror intervals for the Lyapunov exponent. We find that the signs of the Lyapunov exponents changes at least three times when increasing the noise amplitude. We also show numerical evidence that the standard non-rigorous numericalapproximation by finite-time Lyapunov exponents is valid with our model for a sufficiently large number of iterations.Our method is expected to work for a broad class of nonlinear stochastic p