Random attractors for stochastic discrete long wave-short wave resonance equations driven by fractional Brownian motions

Abstract

We study the dynamical behavior of the solutions of stochastic discrete long wave-short wave resonance equations driven by fractional Brownian motions with Hurst parameter $ H\in(\frac{1}{2}, 1) $. And then we prove that the random dynamical system has a unique random equilibrium, which constitutes a singleton sets random attractor.

Keywords

• stochastic discrete long wave-short wave resonance equation
• random attractor
• fractional brownian motion