Multivaluedness aspects in self-organization, complexity and computations investigations by strong anticipation

Abstract

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