# American Institute of Mathematical Sciences

February  2020, 25(2): 799-813. doi: 10.3934/dcdsb.2019268

## Attractors of Hopfield-type lattice models with increasing neuronal input

 1 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China 2 Department of Mathematics and Statistics, Auburn University, Auburn, AL 36832, USA

* Corresponding author: Xiaoli Wang

Dedicated to Juan J. Nieto on the occasion of his 60th birthday

Received  September 2018 Revised  February 2019 Published  November 2019

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

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 $n \to \infty$.

Citation: Xiaoli Wang, Peter E. Kloeden, Xiaoying Han. Attractors of Hopfield-type lattice models with increasing neuronal input. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 799-813. doi: 10.3934/dcdsb.2019268
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