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Hysteresis model of unconscious-conscious interconnection: Exploring dynamics on m-adic trees

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Abstract

In this brief note, we focus attention on a possible implementation of a basic hysteretic pattern (the Preisach one), suitably generalized, into a formal model of unconscious-conscious interconnection and based on representation of mental entities by m-adic numbers.

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Authors and Affiliations

  1. Department of Physics and Chemistry, University of Palermo, I-90128, Palermo, Italy

    G. Iurato

  2. International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science Linnaeus University, S-35195, Växjö, Sweden

    A. Khrennikov

Authors
  1. G. Iurato
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  2. A. Khrennikov
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Correspondence to G. Iurato.

Additional information

The text was submitted by the authors in English.

Mathematically it is fruitful to proceed with the fields of p-adic numbers, where p > 1 is a prime number. These fields play an important role in theoretical physics, string theory, quantum mechanics and field theory, cosmology, see, e.g., [1, 5] for recent reviews. However, in cognitive and psychological applications there are no reasons to restrict models to prime number bases. It is more natural to work with the rings of m-adic numbers, where m > 1 is an arbitrary natural number. Here m determines the number of branches leaving each vertex of the tree representing geometrically the ring of the m-adic numbers. But even models based on such homogeneous trees are too restrictive. Neuronal trees in the brain and the corresponding information trees can be non-homogeneous as well. Such trees are algebraically realized as more complex rings. In general the language of ultrametric spaces covers completely tree-like representations of information in cognitive studies and psychology [21]. However, up to now not so much has been done on general utrametric spaces. It is very convenient and fruitful to have trees endowed with algebraic structures.

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Iurato, G., Khrennikov, A. Hysteresis model of unconscious-conscious interconnection: Exploring dynamics on m-adic trees. P-Adic Num Ultrametr Anal Appl 7, 312–321 (2015). https://doi.org/10.1134/S2070046615040068

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  • DOI: https://doi.org/10.1134/S2070046615040068

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