Ergodicity of stochastic Rabinovich systems driven by fractional Brownian motion

Abstract

The current paper is devoted to dynamics of stochastic Rabinovich systems driven by fractional Brownian motion. By using Krylov–Bogoliubov criterion and constructing of Lyapunov function, the existence of invariant measure of stochastic Rabinovich system is established. The uniqueness of invariant measure is also obtained by the strong Feller property and topological irreducibility. Therefore the considered system possess exactly one invariant measure, which is also an unique adapted stationary solution.