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March  2019, 18(2): 809-824. doi: 10.3934/cpaa.2019039

## Long term behavior of a random Hopfield neural lattice model

 Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA

* Corresponding author

Received  March 2018 Revised  May 2018 Published  October 2018

Fund Project: This work was partially supported by Simons Foundation, USA (Collaboration Grants for Mathematicians No. 429717) and NSF of China (Grant No. 11571125)

A Hopfield neural lattice model is developed as the infinite dimensional extension of the classical finite dimensional Hopfield model. In addition, random external inputs are considered to incorporate environmental noise. The resulting random lattice dynamical system is first formulated as a random ordinary differential equation on the space of square summable bi-infinite sequences. Then the existence and uniqueness of solutions, as well as long term dynamics of solutions are investigated.

Citation: Xiaoying Han, Peter E. Kloeden, Basiru Usman. Long term behavior of a random Hopfield neural lattice model. Communications on Pure & Applied Analysis, 2019, 18 (2) : 809-824. doi: 10.3934/cpaa.2019039
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