Stochastic sensitivity analysis of noise-induced intermittency and transition to chaos in one-dimensional discrete-time systems

Abstract

We study a phenomenon of noise-induced intermittency for the stochastically forced one-dimensional discrete-time system near tangent bifurcation. In a subcritical zone, where the deterministic system has a single stable equilibrium, even small noises generate large-amplitude chaotic oscillations and intermittency. We show that this phenomenon can be explained by a high stochastic sensitivity of this equilibrium. For the analysis of this system, we suggest a constructive method based on stochastic sensitivity functions and confidence intervals technique. An explicit formula for the value of the noise intensity threshold corresponding to the onset of noise-induced intermittency is found. On the basis of our approach, a parametrical diagram of different stochastic regimes of intermittency and asymptotics are given.