Multistate Intermittency

AbstractIrregular switches between two different dynamical regimes, when all system parameters are fixed, is known as intermittency. The concept of intermittency was extended to systems with coexisting states and referred to as multistate intermittency. Such intermittency reveals itself as alternation of equilibrium, periodic or chaotic regimes. The irregular switching between coexisting states can be caused either by random, chaotic, or periodic perturbations. In the former case, we deal with so-called noise-induced intermittency or attractor hopping. Although both names are widely used in the literature, in our opinion, the term “multistate intermittency” more accurately reflects the intermittent nature of this kind of dynamics in systems with coexisting attractors. Intermittency in a multistable system can also be caused by an external force that can be either random or periodic in a chaotic system. Since random fluctuations (or noise) are inevitable in real systems, the interaction between nonlinearity and stochasticity has attracted much attention of various researchers. It was found that adding noise to a multistable system causes many interesting effects, such as noise-induced escapes from equilibria [1, 2], stochastic resonance [3, 4], self-organization [5], multistate intermittency [6], noise-induced preference of attractors [7], extreme events [8], etc. Some of these effects are considered in this section.