# American Institute of Mathematical Sciences

April  2020, 19(4): 2385-2402. doi: 10.3934/cpaa.2020104

## Sigmoidal approximations of a delay neural lattice model with Heaviside functions

 1 School of Mathematics and Statistics and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China 2 Mathematisches Institut, Universität Tübingen, D-72076 Tübingen, Germany

*Corresponding author

Dedicated to Professor Tomás Caraballo on occasion of his 60th Birthday

Received  April 2019 Revised  October 2019 Published  January 2020

Fund Project: This work was partially supported by the NSF of China Grant No. 11971184.

The approximation of Heaviside coefficient functions in delay neural lattice models with delays by sigmoidal functions is investigated. The solutions of the delay sigmoidal models are shown to converge to a solution of the delay differential inclusion as the sigmoidal parameter goes to zero. In addition, the existence of global attractors is established and compared for the various systems.

Citation: Xiaoli Wang, Meihua Yang, Peter E. Kloeden. Sigmoidal approximations of a delay neural lattice model with Heaviside functions. Communications on Pure & Applied Analysis, 2020, 19 (4) : 2385-2402. doi: 10.3934/cpaa.2020104
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