Attractors for second order nonautonomous lattice system with dispersive term

Rank One Attractors in a Periodically Perturbed Second Order System

In this paper we study a time dependent second order system in the form of dq dt2 + (a− bq2) dt − q + q = μ sinωt where a > 0, b, μ, ω are parameters. We prove that this equation admits strange attractors with SRB measures for a positive measure set of parameters (a, b, μ, ω). Periodically perturbed second order systems have been studied extensively in the history of the modern theory of chaos ...

Attractors for Nonautonomous Parabolic Equations without Uniqueness

Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. The Kneser property of solutions is also studied, and as a result we obtain the connec...

Uniform Nonautonomous Attractors under Discretization

A nonautonomous or cocycle dynamical system that is driven by an autonomous dynamical system acting on a compact metric space is assumed to have a uniform pullback attractor. It is shown that discretization by a one-step numerical scheme gives rise to a discrete time cocycle dynamical system with a uniform pullback attractor, the component subsets of which converge upper semi continuously to th...

On the property of for a second-order system with zero diagonal coefficient

Abstract: This paper investigates the problem of whether all trajectories of the system and cross the vertical isocline, which is very important for the existence of periodic solutions and oscillation theory. Sufficient conditions are given for all trajectories to cross the vertical isocline.  

Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations