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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.

37N99 Applications of dynamical systems
94B40 Arithmetic codes
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