Interacting Dynamics

TL;DR

This paper introduces a new unified theory of interacting generalized dynamical systems, expanding the framework with concepts like normal and concrete interactions, and replacing rigid synchronizations with flexible ones.

Contribution

It presents a comprehensive, unified presentation of the theory of open sub-functorial dynamics, including new concepts and more general interaction mechanisms.

Findings

Introduction of normal and concrete interactions

Replacement of rigid synchronizations with flexible ones

Illustrative examples of the new framework

Abstract

The "theory of open sub-functorial dynamics" is a new theory that defines interacting generalized dynamical systems. The interactions between these dynamics produce new dynamics which, of course, can then enter into other interactions. A major part of this article can already be found in two unpublished texts and it has been partially exposed in conferences. However, we need to give a new, unified and therefore more convenient presentation of this material, and we also need some examples to illustrate it. Moreover, we introduce in this article the new concepts of "normal interaction" and "concrete interaction", and replace the previously used rigid synchronizations by much more general flexible ones.