Long term behavior of a random Hopfield neural lattice model
Xiaoying Han, Peter E. Kloeden, Basiru Usman · Communications on Pure & Applied Analysis · 2018
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.