We deene point attractors and set attractors for random dynamical systems via convergence in probability forward in time. This deenition of a set attractor is weaker than the usual one via almost sure pullback convergence. We derive basic properties of our weak random attractors such as uniqueness, support of invariant measures and invari-ance under (random) coordinate transformations. The noti...

We show the existence of an exponential attractor for non-autono-mous dynamical system with bounded delay. considered case strong dissipativity then prove that result remains weak dissipativity. conclude global and ensure boundedness its fractal dimension.

The construction of attractors a dissipative difference equation is usually based on compactness assumptions. In this paper, we replace them with contractivity assumptions under which the pullback and forward are identical. As consequence, degenerate to unique bounded entire solutions. an application, investigate integrodifference equations popular models in theoretical ecology.

First, for a process {U(t, τ)∣t ≥ τ}, we introduce a new concept, called the weak D-pullback exponential attractor, which is a family of sets {ℳ(t)∣t ≤ T}, for any T ∈ ℝ, satisfying the following: (i) ℳ(t) is compact, (ii) ℳ(t) is positively invariant, that is, U(t, τ)ℳ(τ) ⊂ ℳ(t), and (iii) there exist k, l > 0 such that dist(U(t, τ)B(τ), ℳ(t)) ≤ ke (-(t-τ)); that is, ℳ(t) pullback exponential ...

This paper investigates the dynamics of a class three-dimensional globally modified Navier–Stokes equations with double delay in forcing and convective terms. We first prove well-posedness solutions such system, which enables us to establish suitable non-autonomous dynamical systems. then show existence uniqueness pullback attractors for associated Finally, by using generalized Banach limit, we...

In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, some models such as reaction–diffusion equations, p-Laplace equation porous media are established.