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