Long term behavior of a random Hopfield neural lattice model

Xiaoying Han; Peter E. Kloeden; Basiru Usman

doi:10.3934/cpaa.2019039

Article Contents

2019, Volume 18, Issue 2: 809-824. Doi: 10.3934/cpaa.2019039

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Long term behavior of a random Hopfield neural lattice model

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

* Corresponding author
* Corresponding author

Received: February 28, 2018

Revised: April 30, 2018

Published: October 2018

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 34D45, 34F05, 37L60, 47J05; Secondary: 92C20, 92C42.

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