Random attractors forstochastic FitzHugh-Nagumo systemsdriven by deterministic non-autonomous forcing

By A. Adili, Bixiang Wang. 2012

66 citations recorded by the source corpus.

This paper is concerned with the asymptotic behavior of solutions of the FitzHugh-Nagumo system on $\mathbb{R}^n$ driven by additive noise and deterministic non-autonomous forcing. We prove the system has a random attractor which pullback attracts all tempered random sets. We also prove the periodicity of the random attractor when the system is perturbed by time periodic forcing. The pullback asymptotic compactness of solutions is established by uniform estimates on the tails of solutions outside a large ball in $\mathbb{R}^n$.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/102c88e884a6acdeb2ac6765e8ff1cbbb7cb0e53

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Computer Networks and Communications

In Control and Systems Engineering

Citations in the corpus

Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains (2013, background): “7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31] in bounded domains, and in [4, 33, 34] in unbounded domains. For non-autonomous stochastic PDEs, the reader is referred to [1, 5, 12, 17, 23, 24, 27, 35, 36, 37] for existence of random attractors. The rest of this article ”
Asymptotic behavior of random fitzhugh-nagumo systems driven by colored noise (2017, background): “The concept of random attractors was introduced in [18, 21, 44] and further studied in [6, 7, 8, 9, 11, 12, 13, 15, 16, 18, 22, 23, 24, 26, 32, 37, 40, 50, 51] for the autonomous stochastic equations; and in [2, 14, 19, 27, 28, 52, 53, 54] for the non-autonomous stochastic equations.”