Global Attractors for Multivalued Random Dynamical Systems Generated by Random Differential Inclusions with Multiplicative Noise

Strange nonchaotic attractors in random dynamical systems.

Whether strange nonchaotic attractors (SNAs) can occur typically in dynamical systems other than quasiperiodically driven systems has long been an open question. Here we show, based on a physical analysis and numerical evidence, that robust SNAs can be induced by small noise in autonomous discrete-time maps and in periodically driven continuous-time systems. These attractors, which are relevant...

Random Attractors for Stochastic Retarded Lattice Dynamical Systems

and Applied Analysis 3 It is worth mentioning that in the absence of the white noise, the existence of a global attractor for 1.3 1.4 was established in 40 . The main contribution of this paper is to extend the method of tail estimates to stochastic retarded LDSs and prove the existence of a random attractor for the infinite dimensional random dynamical system generated by stochastic retarded L...

Exponential attractors for random dynamical systems and applications

The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE’s. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then apply these results to a nonlinear reaction-diffusion system with a random perturbation. We show, in particular, that the attractors can be constru...

Synchronization by Noise for Order-preserving Random Dynamical Systems

We provide sufficient conditions for weak synchronization/stabilization by noise for order-preserving random dynamical systems on Polish spaces. That is, under these conditions we prove the existence of a weak point attractor consisting of a single random point. This generalizes previous results in two directions: First, we do not restrict to Banach spaces and second, we do not require the part...

Random Attractors for Stochastic Three-Component Reversible Gray-Scott System with Multiplicative White Noise