Delay-Controlled Reactions

TL;DR

This paper explores how delay-controlled feedback mechanisms, both external and internal, influence reaction dynamics, leading to novel behaviors such as persistent solutions and finite stationary concentrations.

Contribution

It introduces a framework for incorporating non-Markovian memory effects into reaction rate equations, revealing new stationary states due to internal feedback mechanisms.

Findings

Internal feedback can produce persistent solutions in reaction dynamics.

External feedback alters the dynamical process without changing fixed points.

Reactions can reach finite stationary concentrations due to feedback effects.

Abstract

When the entities undergoing a chemical reaction are not available simultaneously, the classical rate equation of a reaction or, alternatively for the evolution of a population, should be extended by including non-Markovian memory effects. We consider the two cases of an external feedback, realized by fixed functions and an internal feedback originated in a self-organized manner by the relevant concentration itself. Whereas in the first case the fixed points are not changed, although the dynamical process is altered, the second case offers a complete new behaviour, characterized by the existence of a time persistent solution. Due to the feedback the reaction may lead to a finite concentration in the stationary limit even in case of a single-species pair annihilation $A + A \to 0$ process. We argue that the different cases are similar to a coupling of additive or multiplicative noises in stochastic processes.