The Study of Mathematical Models for Self-Organizing Systems

摘要

Emphasis of the work is concentrated on three of the more promising models of self-organizing systems; namely, the cellular model, the linear statistical model and the list structure model. The discussion of the cellular model describes experiments in a two-dimensional rectangular space initially containing binary elements. The experiments gave insight into rules of element behavior that lead to stability and pattern formation. The linear statistical predictor provides a method for determining the structures of time-varying systems within a behavioral class. The list structure model began with an examination of state classes and regular expressions. It became clear early in the study that a primary prerequisite was a language suited to description of such a model capable of being programmed on a computer. It was demonstrated that the second-order predicate logic was a suitable language.