Pullback Attractors for the Non-autonomous FitzHugh-Nagumo System on Unbounded Domains

2008/05/24 by Bixiang Wang, Wang, Bixiang
Computer Science · Engineering · Mathematics · #35B40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.0805.3746

openalex publication_date 2008/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The existence of a pullback attractor is established for the singularly perturbed FitzHugh-Nagumo system defined on the entire space Rⁿ when external terms are unbounded in a phase space. The pullback asymptotic compactness of the system is proved by using uniform a priori estimates for far-field values of solutions. Although the limiting system has no global attractor, we show that the pullback attractors for the perturbed system with bounded external terms are uniformly bounded, and hence do not blow up as a small parameter approaches zero.

Citations

• Random dynamical systems
• Impulses and Physiological States in Theoretical Models of Nerve Membrane
• ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS

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