Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models

Ricardo Bioni Liberalquino, Maurizio Monge, Stefano Galatolo and Luigi Marangio
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Ricardo Bioni Liberalquino: Institute of Mathematics, Universidade Federal do Rio de Janeiro, 21941-901 Rio de Janeiro, Brazil
Maurizio Monge: Institute of Mathematics, Universidade Federal do Rio de Janeiro, 21941-901 Rio de Janeiro, Brazil
Stefano Galatolo: Dipartimento di Matematica, Università di Pisa, 56126 Pisa, Italy
Luigi Marangio: Femto-ST Institute, Université de Université Bourgogne Franche-Comté, 21000 Dijon, France

Mathematics, 2018, vol. 6, issue 3, 1-10

Abstract: 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.

Keywords: chaotic itineracy; computer aided proof; neural networks (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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