Dynamics with choice

TL;DR

This paper introduces and explores the concept of dynamics with choice, a generalization of discrete-time systems allowing multiple evolution operators, with applications across various scientific fields.

Contribution

It presents the notion of dynamics with choice as a new mathematical framework and investigates its long-term behavior, bridging theory and real-world applications.

Findings

New mathematical framework for systems with multiple evolution operators

Analysis of long-term behavior in dynamics with choice

Relevance to biological, chemical, and engineering systems

Abstract

Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. This notion is new and interesting from the mathematical point of view. At the same time, many real life processes studied in chemical physics, engineering, biology and medicine, from autocatalytic reaction systems to switched systems to cellular biochemical processes to malaria transmission in urban environments, exhibit the properties described by dynamics with choice. We study the long-term behavior in dynamics with choice.