Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models

被引：2

作者：

Liberalquino, Ricardo Bioni ^{[1
]}

Monge, Maurizio ^{[1
]}

Galatolo, Stefano ^{[2
]}

Marangio, Luigi ^{[3
]}

机构：

[1] Univ Fed Rio de Janeiro, Inst Math, BR-21941901 Rio De Janeiro, Brazil

[2] Univ Pisa, Dipartimento Matemat, I-56126 Pisa, Italy

[3] Univ Univ Bourgogne Franche Comte, Femto ST Inst, F-21000 Dijon, France

来源：

MATHEMATICS | 2018年 / 6卷 / 03期

关键词：

chaotic itineracy; computer aided proof; neural networks; NEURAL-NETWORKS; MAP;

D O I：

10.3390/math6030039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a random dynamical system arising as a model of the behavior of a macrovariable related to a more complicated model of associative memory. This system can be seen as a small (stochastic and deterministic) perturbation of a determinstic system having two weak attractors which are destroyed after the perturbation. We show, with a computer aided proof, that the system has a kind of chaotic itineracy. Typical orbits are globally chaotic, while they spend a relatively long time visiting the attractor's ruins.

引用

页数：10

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