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.

引用

下载

页码：4683 / 4691

页数：9

共 50 条

[41] Strong law of large numbers for discrete-time and continuous-state nonhomogeneous Markov chains
Faculty of Science, Jiangsu University, Zhenjiang 212013, China
Jiangsu Daxue Xuebao Ziran Kexue Ban J. Jiangsu Univ. Nat. Sci. Ed., 2008, 1 (86-88):
[42] An implicit representation for the analysis of piecewise affine discrete-time systems
Groff, Leonardo Broering
Valmorbida, Giorgio
da Silva, Joao Manoel Gomes
AUTOMATICA, 2023, 147
[43] Feedback control design for discrete-time piecewise affine systems
XU Jun1
2.School of Electrical and Electronic Engineering
山东大学学报(工学版), 2007, (03) : 1 - 10
[44] Stabilization of Discrete-time Piecewise Affine Systems with Quantized Signals
Wakaiki, Masashi
Yamamoto, Yutaka
2015 54TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2015, : 1601 - 1606
[45] Optimal Control of Constrained Piecewise Affine Discrete-Time Systems
D. Q. Mayne
S. Raković
Computational Optimization and Applications, 2003, 25 : 167 - 191
[46] Optimal control of constrained piecewise affine discrete-time systems
Mayne, DQ
Rakovic, S
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2003, 25 (1-3) : 167 - 191
[47] Temporal Logic Control of Discrete-Time Piecewise Affine Systems
Yordanov, Boyan
Belta, Calin
PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, : 3182 - 3187
[48] Temporal Logic Control of Discrete-Time Piecewise Affine Systems
Yordanov, Boyan
Tumova, Jana
Cerna, Ivana
Barnat, Jiri
Belta, Calin
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2012, 57 (06) : 1491 - 1504
[49] Feedback control design for discrete-time piecewise affine systems
Xu, J
Xie, LH
Feng, G
2005 INTERNATIONAL CONFERENCE ON CONTROL AND AUTOMATION (ICCA), VOLS 1 AND 2, 2005, : 425 - 430
[50] Stabilization of Discrete-Time Piecewise Affine Systems in Implicit Representation
Cabral, L.
da Silva Jr, J. M. Gomes Jr
Valmorbida, G.
2021 60TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2021, : 6049 - 6054

← 1 2 3 4 5 →