Almost Periodic Dynamics of Perturbed Infinite-Dimensional Dynamical Systems

2011/03/11 by Bixiang Wang, Wang, Bixiang
Computer Science · Engineering · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1103.2371

openalex publication_date 2011/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable manifolds of a finite number of hyperbolic equilibrium solutions, we prove that the perturbed non-autonomous system has exactly the same number of almost periodic solutions. As a consequence, the pullback attractor of the perturbed system is given by the union of unstable manifolds of these finitely many almost periodic solutions. An application of the result to the Chafee-Infante equation is discussed.

Related

• Stability problems in non autonomous linear differential equations in infinite dimensions
• Global attractivity in almost periodic single species models
• On the Structure of the Global Attractor for Non-autonomous Difference Equations with Weak Convergence
• Global attractivity of almost periodic solutions for competitive\n Lotka-Volterra diffusion system
• Attractors and global averaging of non-autonomous reaction-diffusion equations in Rⁿ