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Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models

Author

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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)

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.

Suggested Citation

  • Ricardo Bioni Liberalquino & Maurizio Monge & Stefano Galatolo & Luigi Marangio, 2018. "Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models," Mathematics, MDPI, vol. 6(3), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:3:p:39-:d:135177
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    References listed on IDEAS

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    1. Leon Glass, 2001. "Synchronization and rhythmic processes in physiology," Nature, Nature, vol. 410(6825), pages 277-284, March.
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