The purpose of this review-and-research paper is twofold:(i) to review the role played in
climate dynamics by fluid-dynamical models; and (ii) to contribute to the understanding and …

The existence of a pullback attractor is established for a stochastic reaction–diffusion
equation on all n-dimensional space. The nonlinearity is dissipative for large values of the …

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial
differential equations with slow and fast time scales, or large and small spatial scales. The …

Invariant manifolds provide the geometric structures for describing and understanding
dynamics of nonlinear systems. The theory of invariant manifolds for both finite-and infinite …

This paper is concerned with the asymptotic behaviour of solutions to a class of non-
autonomous stochastic nonlinear wave equations with dispersive and viscosity dissipative …

Transitions between regimes with radically different properties are ubiquitous in nature.
Such transitions can occur either smoothly or in an abrupt and catastrophic fashion …

The existence of a random attractor in $ H^ 1 (\mathbb {R}^ 3)\times L^ 2 (\mathbb {R}^ 3) $
is proved for the damped semilinear stochastic wave equation defined on the entire space …

Invariant manifolds are fundamental tools for describing and understanding nonlinear
dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite …

We prove the existence of a compact random attractor for the stochastic Benjamin–Bona–
Mahony equation defined on an unbounded domain. This random attractor is invariant and …

There is a vast body of literature devoted to the study of bifurcation phenomena in
autonomous systems of differential equations. However, there is currently no well-developed …