Maximal Global Random Attractors of Gradient-Like Random Dynamical Systems by Stochastic Lyapunov Functions

Resumen

This paper investigates the existence and construction of the maximal attractors of gradient-like random dynamical systems (RDSs), assuming the system is asymptotically compact, admits a Lyapunov function, and the set of equilibrium points is bounded. The study begins by presenting a stochastic version of  LaSalle’s Invariance Principle, followed by an analysis of the random Levinson center for gradient RDSs with finite number of equilibrium points.