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$$p$$-adic discrete dynamical systems and collective behaviour of information states in cognitive models. (English) Zbl 1229.37128
Summary: We develop a model of functioning of complex information systems (in particular, cognitive systems) in that information states are coded by $$p$$-adic integers. An information state evolves by iterations of a discrete $$p$$-adic dynamical system. The $$p$$-adic utrametric on the space of information states ($$p$$-adic homogeneous tree) describes the ability of an information system to operate with associations. The main attention is paid to the collective dynamics of families of associations.

##### MSC:
 37N99 Applications of dynamical systems 94B40 Arithmetic codes
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