KINETICS OF DICHOTOMOUS NOISE-INDUCED TRANSITIONS IN A MULTISTABLE MULTIVARIATE SYSTEM

We study the stochastic evolution of a multivariate and deterministica lly multistable system subjected to an additive Markovian dichotomous noise. To this end, a steady-state probability density support is defi ned in such a way that no stochastic trajectory can escape. An appropr iate boundary condition is then imposed in order to numerically evalua te this distribution. When the noise amplitude is large enough, the sy stem may evolve from one deterministic attractor to another. A partiti on of the support in disjoint species is proposed. It is then possible to study the kinetics of the noise-induced transitions between specie s. Projection operator techniques are used to obtain a phenomenologica l kinetic law valid when the interspecies transition time scale is muc h longer than all the other time scales characterizing the system. We also develop a fast algorithm permitting the numerical evaluation of t he phenomenological transition rate. As an example, we consider a biva riate system exhibiting two deterministic stable fixed points and a sa ddle point. The results confirm the existence of a phenomenological la w insofar as the noise amplitude is large enough and its correlation t ime, small enough.