In this paper we prove an upper semicontinuity result for perturbations of cocycle attractors. In particular, we study relationship between non-autonomous and global attractors. In this sense, we show that the concept of a cocycle attractor is a sensible generalization to non-autonomous and random dynamical systems of that of the global attractor.

We extend previous results on the existence of the global attractor for the 2D Navier-Stokes equations on some unbounded domains in the sense that the forcing term need not lie in any weighted space nor is the boundary of the domain required to be smooth. The existence of the global attractor is obtained on arbitrary open sets such that the Poincaré inequality holds and for forces in the natura...

Abstract: This paper aims at presenting a proof of the attractor for a class of viscous nonlinear dispersive wave equations. In this paper, the global existence of solution to this equation in L2 under the periodical condition is studied. By using the time estimate of this equation, we get the compact and bounded absorbing set and the existence of the global attractor for the viscous nonlinear ...

A new 3D autonomous dynamical system proposed by Dequan Li [Physics Letters A, 372, 387, 2008.] produces a chaotic attractor whose global topological properties are unusual. The attractor has a rotation symmetry and only a single real fixed point for the parameters used in his study. The symmetric, complex pair of fixed points cannot be ignored: they play a major role in organizing the motion o...

We study in this article the bifurcation and stability of the solutions of the Ginzburg–Landau equation, using a notion of bifurcation called attractor bifurcation. We obtain in particular a full classification of the bifurcated attractor and the global attractor as λ crosses the first critical value of the linear problem. Bifurcations from the rest of the eigenvalues of the linear problem are ...