### Electronic Research Archive

2020, Issue 2: 1037-1048. doi: 10.3934/era.2020056
Special Issues

# Asymptotic behaviour of a neural field lattice model with delays

• Received: 01 March 2020 Revised: 01 April 2020
• Primary: 34A33, 34D05; Secondary: 35B41, 92B20

• 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[J]. Electronic Research Archive, 2020, 28(2): 1037-1048. doi: 10.3934/era.2020056

### Related Papers:

• 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.

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