Multivaluedness Aspects in Self-organization, Complexity and Computations Investigations by Strong Anticipation

TL;DR

This paper explores multivalued solutions in strongly anticipatory discrete dynamical systems, highlighting their complex behaviors, attractor properties, and implications for automata theory and hypercomputation.

Contribution

It introduces new examples and analytical approaches for systems with strong anticipation, emphasizing multivaluedness and complex dynamics in automata.

Findings

Examples of periodic and complex solutions are presented.

Attractor properties and potential applications in self-organization are discussed.

The paper suggests new directions for automata theory and hypercomputation.

Abstract

Since the introduction of strong anticipation by D.~Dubois the numerous investigations of concrete systems have been proposed. In proposed paper the new examples of discrete dynamical systems with anticipation are considered. The mathematical formulation of problems, possible analytical formulas for solutions and numerical examples of presumable solutions are proposed. One of the most interesting properties in such systems is presumable multivaluedness of the solutions. It can be considered from the point of view of dynamical chaos and complex behavior. We represent examples of periodic and complex solutions, attractor's properties and presumable applications in self-organization. The main peculiarity is the strong anticipation property. General new possibilities are the presumable multivaluedness of the dynamics of automata. Possible interpretations of such behavior of cellular automata are discussed. Further prospects for development of automata theory and hyper computation are proposed.