Regular Attractor by Strict Lyapunov Function for Random Dynamical Systems

The main objective of this paper is to study some types of random attractors in random dynamical systems based on the random strict Lyapunov function. Where we first defined the random strict Lyapunov function and then the definition of the gradient random dynamical system and studied the finding of global attractors based on the existence of the random strict Lyapunov function. Last but not least, we introduced a new type of random attractor, which we called the random regular attractor, and proved the relationship between the existence of a regular attractor and the existence of a random strict Lyapunov function.