\(p\)-adic discrete dynamical systems and collective behaviour of information states in cognitive models. (English) Zbl 1229.37128

Khrennikov, Andrei

Discrete Dyn. Nat. Soc. 5, No. 1, 59-69 (2000).

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

Keywords:

\(p\)-adic trees; dynamical systems; cognitive models; hierarchic thinning