# American Institute of Mathematical Sciences

June  2020, 28(2): 1037-1048. doi: 10.3934/era.2020056

## Asymptotic behaviour of a neural field lattice model with delays

 1 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China 2 Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong, University of Science and Technology, Wuhan 430074, China

* Corresponding author: Meihua Yang

Received  March 2020 Revised  April 2020 Published  June 2020

Fund Project: The authors are supported by the NSFC grant 11971184

The asymptotic behaviour of an autonomous neural field lattice system with delays is investigated. It is based on the Amari model, but with the Heaviside function in the interaction term replaced by a sigmoidal function. First, the lattice system is reformulated as an infinite dimensional ordinary delay differential equation on weighted sequence state space $\ell_\rho^2$ under some appropriate assumptions. Then the global existence and uniqueness of its solution and its formulation as a semi-dynamical system on a suitable function space are established. Finally, the asymptotic behaviour of solution of the system is investigated, in particular, the existence of a global attractor is obtained.

Citation: Xiaoli Wang, Peter Kloeden, Meihua Yang. Asymptotic behaviour of a neural field lattice model with delays. Electronic Research Archive, 2020, 28 (2) : 1037-1048. doi: 10.3934/era.2020056
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