Beyond Chaos

TL;DR

This paper introduces a mathematical framework for recursive interactions using logistic functions, defines new types of attractors, and shows through experiments that such systems can transition from chaos to order.

Contribution

It presents a novel theoretical approach to recursive interactions, introduces orbital attractors, and provides experimental evidence of chaos-to-order transitions.

Findings

Interacting systems can evolve from chaos to order.

Orbital attractors include irregular and complex orbits.

Recursive interactions can be modeled with logistic functions.

Abstract

The first part of this paper defines recursive interactions by means of logistic functions and derives a general result on the way interacting systems evolve in attractors. It also defines the notion of coevolution trajectory and presents a new family of attractors: orbital attractors (including single, irregular, folded, complex and discontinuous orbits). The second part summarizes the results of a first experimental analysis of recursive interactions in both binary and multiple interactions. Among other results, this analysis reveals that interacting systems may easily evolve from chaos to order.