Statistical characteristics of noise-induced intermittency in multistable systems

The paper is devoted to the study of noise-induced intermittent behavior in multistable systems. Such task is an important enough because despite of a great interest of investigators to the study of multistability and intermittency, the problem connected with the detailed understanding of the processes taking place in the multistable dynamical systems in the presence of noise and theoretical description of arising at that intermittent behavior is still remain unsolved. In present paper we analyze the noise-induced intermittency in multistable systems using the examples of model bistable system being under influence of external noise and two dissipatively coupled logistic maps subjected to additional noise. We have shown that the influence of noise on multistable system for certain values of the control parameters results in the appearance of noise-induced intermittent behavior. At that, for the found type of intermittent behavior the analytical relations for residence time distributions and dependence of the mean length of the residence times on the criticality parameter have been obtained. During the numerical simulations carried out we have found statistical characteristics for such type of intermittency for both systems, i.e. the distributions of the residence times for both coexisting stable states as well as the dependence of the mean length of the residence times for both regimes on the criticality parameter. The results of numerical simulation of intermittent behavior for systems under study have been compared with the obtained analytical regularities for noise-induced intermittency in multistable systems. At that, we have shown that numerical results and theoretical regularities are in a good agreement with each other.