Attractors of Hopfield-type lattice models with increasing neuronal input

Abstract

Dedicated to Juan J. Nieto on the occasion of his 60th birthday Abstract. Two Hopfield-type neural lattice models are considered, one with local n-neighborhood nonlinear interconnections among neurons and the other with global nonlinear interconnections among neurons. It is shown that both systems possess global attractors on a weighted space of bi-infinite sequences. Moreover, the attractors are shown to depend upper semi-continuously on the interconnection parameters as n → ∞.

Stochastic dynamics of a neural field lattice model with state dependent nonlinear noise

“…Recent studies on X. Wang et al NoDEA neural lattice models include the traveling fronts for a class of lattice neural field equations by Faye [16], long term dynamics for neural field lattice models by Han and Kloeden [21,22], Wang et al [36,38], long term dynamics for Hopfiled-type neural lattice models by Han et al [23,24], Wang et al [35]. Most recently, Sui et al studied the existence and structure of random attractors for a neural lattice model with delays [29].…”

Asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise

“…Up to now, long-range interaction has been studied for different physical systems. For examples, traveling wave solution for lattice model with infinite-range interaction can be found in [3,36], the continuum limit for discrete nonlinear Schrödinger equations with long-range lattice interactions are considered in [26,27], attractors of neural lattice model are studied in [23,24,34] for finite-range interaction and [22,39] for infinite-range interaction.…”

“…It is worth mentioning that the fractional discrete Laplacian (−∆ d ) s is nonlocal and hence deriving uniform estimates on the tails of solutions are much more involved than the discrete Laplacian −∆ d . In addition, lattice with fractional discrete Laplacian is different from the neural networks lattice with long-range interaction that are considered in [22,23,24,34,39].…”