Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models
1
Institute of Mathematics, Universidade Federal do Rio de Janeiro, 21941-901 Rio de Janeiro, Brazil
2
Dipartimento di Matematica, Università di Pisa, 56126 Pisa, Italy
3
Femto-ST Institute, Université de Université Bourgogne Franche-Comté, 21000 Dijon, France
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(3), 39; https://doi.org/10.3390/math6030039
Received: 31 January 2018 / Revised: 26 February 2018 / Accepted: 28 February 2018 / Published: 7 March 2018
(This article belongs to the Special Issue Chaos and Randomness of Discrete Dynamical Systems: Their Use in Applied Science)
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.
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Keywords:
chaotic itineracy; computer aided proof; neural networks
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MDPI and ACS Style
Bioni Liberalquino, R.; Monge, M.; Galatolo, S.; Marangio, L. Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models. Mathematics 2018, 6, 39. https://doi.org/10.3390/math6030039
AMA Style
Bioni Liberalquino R, Monge M, Galatolo S, Marangio L. Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models. Mathematics. 2018; 6(3):39. https://doi.org/10.3390/math6030039
Chicago/Turabian StyleBioni Liberalquino, Ricardo; Monge, Maurizio; Galatolo, Stefano; Marangio, Luigi. 2018. "Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models" Mathematics 6, no. 3: 39. https://doi.org/10.3390/math6030039
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