Article

# Fixed points incompatibility in neural networks with local interactions

Istituto di Elettronica, Perugia Univ.
IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications 07/1995; DOI:10.1109/81.390274
Source: IEEE Xplore

ABSTRACT Two conditions of incompatibility between fixed points are proved,
which hold for a wide class of discrete-time, discrete-state, nonlinear
neural networks with local interactions and no self-feedback. These
conditions, which can be checked easily by inspection, can be stated
briefly as follows: Let the network be defined on a two-dimensional
array. A pair of states cannot both be fixed points of the network
dynamics if: (1) in the neighborhood of a different component, there is
no other different component; and (2) in the neighborhood of an equal
component, there is no other equal component

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### Keywords

conditions

different component

equal component

local interactions

neighborhood

neural networks

points

self-feedback

states

wide class