Bifurcations in Cognitive Networks: A Paradigm of Self-organization via Desynchronization

Abstract

The concept of “synchronization” is employed as an index of good organization in usual (“preallocation”) communication networks; it should be relaxed though and enlarged in cognitive networks (which are hierarchical structures) in order to incorporate dynamical deliberations taking place in “dynamic allocation” or packet — switching networks, finite state automata as well as biological, ecological economic and social systems.

Here the need to deal with decision making algorithms which involve hierarchical control of competitive processes becomes imperative. In such systems “self” — organization can occur as a result of bifurcation processes triggered by learning.

These processes may lead via destabilization of the old control strategy to the abrupt emergence of a metalanguage or a new decision making algorithm among the members — “users” of the system at the expense perhaps of temporal or spatial coherence among the interacting partners. The result of such a “catastrophe” is a richer perceptive and behavioral repertoire of the system and an amelioration of his adaptability to “noisy” environments. In that sense the system “Soviet Union” is more synchronized but the system “United States” is more organized. In short the way we envisage the role of organization in a “cognitive network” of interacting variables (organisms) — performing under conditions of uncertainty and conflict has not so much to do with the congruence between the sequences of behavioral mode turnover of the individual subsystems constituting the networks: it has rather to do with the solution of a dual objective optimization problem compromizing defacto conflicting factors such as homeostasis (e.g. persistence at a given state) and adequate crosscorrelations with the partner — subsystem.

The whole idea is fully developed in the present paper in a simple network consisting of two interacting hierarchical subsystems.

Each subsystem — organism posessessin turn two irreducible hierarchical levels playing the role of “store — forward” and “traffic” processes or “behavior” and “experience” respectively.

The evolution of the system is pursued in a unifying contentless formalism of inductively played nonnegotiable games between the hierarchical levels of each partner — subsystem.

A detailed isomorphic model concerning nonresolvable ambiguity of communication dynamics (envisaged as bidirectional information transfer) between two hierarchical structures, is worked out.

The scope is to design feed forward control algorithms leading to limited resolution of the intrasystemic conflict via inter systemic communication.