A CHAOTIC DISCRETE-TIME CONTINUOUS-STATE HOPFIELD NETWORK WITH PIECEWISE-AFFINE ACTIVATION FUNCTIONS

被引：0
|
作者：
Pires, Benito [1 ]
机构：
[1] Univ Sao Paulo, Fac Filosofia Ciencias & Letras, Dept Comp & Matemat, BR-14040901 Ribeirao Preto, SP, Brazil
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2023年 / 28卷 / 09期
基金：
巴西圣保罗研究基金会;
关键词：
Hopfield network; chaotic neural network; piecewise-affine activation function; Cantor attractor; SPARSE AUTOENCODERS; NEURAL-NETWORKS; DYNAMICS;
D O I：
10.3934/dcdsb.2023035
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct a chaotic discrete-time continuous-state Hopfield network with piecewise-affine nonnegative activation functions and weight matrix with small positive entries. More precisely, there exists a Cantor set C in the state space such that the network has sensitive dependence on initial conditions at initial states in C and the network orbit of each initial state in C has C as its omega-limit set. The approach we use is based on tools developed and employed recently in the study of the topological dynamics of piecewise-contractions. The parameters of the chaotic network are explicitly given.
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页码：4683 / 4691
页数：9
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