title: Analysis of continuous attractors for 2-D linear threshold neural networks.
abstract: This brief investigates continuous attractors of the well-developed model in visual cortex, i.e., the linear threshold (LT) neural networks, based on a parameterized 2-D model. On the basis of existing results on nondegenerate equilibria in mathematics, we further discuss degenerate equilibria for such networks and present properties and distributions of the equilibria, which enables us to draw the coexistence conditions of nondegenerate and degenerate equilibria (e.g., singular lines). Our theoretical results provide a useful framework for precise tuning on the network parameters, e.g., the feedbacks and visual inputs. Simulations are also presented to illustrate the theoretical findings.
authors.affiliation: Yangtze Center of Mathematics and the Department of Mathematics, Sichuan University, Chengdu 610064, China. lanzou@yahoo.com.cn
authors.forename: Lan
authors.initials: L
authors.lastname: Zou
authors.forename: Huajin
authors.initials: H
authors.lastname: Tang
authors.forename: Kay Chen
authors.initials: KC
authors.lastname: Tan
authors.forename: Weinian
authors.initials: W
authors.lastname: Zhang
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D005246:Feedback; D016014:Linear Models; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009434:Neural Pathways / Q000502:physiology; D014793:Visual Cortex / Q000502:physiology