Asymptotic Behavior of neural fields in an unbounded domain

Severino Horacio da Silva; Michel Barros Silva

Asymptotic Behavior of neural fields in an unbounded domain

Dynamical Systems 2013-12-31 v1

Authors: Severino Horacio da Silva , Michel Barros Silva

Abstract

In this paper, we prove the existence of a compact global attractor for the flow generated by equation $\frac{\partial u}{\partial t}(x,t)+u(x,t)= \int_{\mathbb{R}^{N}}J(x-y)(f( u(y,t))dy+ h, \quad h > 0, \quad x\in \mathbb{R}^{N}, \quad t\in\mathbb{R}_{+}$ in the weight space $L^{p}(\mathbb{R}^{N}, \rho)$ . We also give uniform estimates on the size of the attractor and we exhibit a Lyapunov functional to the flow generated by this equation

Keywords

neural fields asymptotic behavior unbounded domain compact global attractor integral equations weighted space Lyapunov functional

Cite

@article{arxiv.1312.7484,
  title  = {Asymptotic Behavior of neural fields in an unbounded domain},
  author = {Severino Horacio da Silva and Michel Barros Silva},
  journal= {arXiv preprint arXiv:1312.7484},
  year   = {2013}
}