Chemical Oscillations out of Chemical Noise

TL;DR

This paper demonstrates that intrinsic chemical noise can induce oscillations and chaos in simple chemical systems, phenomena that are absent in mean-field models, with implications for understanding extinction events.

Contribution

It introduces a large deviation theory-based Hamiltonian framework to show noise-induced oscillations and chaos in low-dimensional chemical systems.

Findings

Intrinsic fluctuations can sustain oscillations and chaos.

Noise can induce behaviors absent in mean-field dynamics.

Phenomena are transient and occur after long waiting times.

Abstract

The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally introduced, which allows developing a Hamiltonian dynamical system able to describe the system dynamics. Using this technique we are able to show that the intrinsic fluctuations, originated in the discrete character of the reagents, may sustain oscillations and chaotic trajectories which are impossible when these fluctuations are disregarded. An important point is that oscillations and chaos appear in systems whose mean-field dynamics has too low a dimensionality for showing such a behavior. In this sense these phenomena are purely induced by noise, which does not limit itself to shifting a bifurcation threshold. On the other hand, they are large deviations of a short transient nature which typically only appear after long waiting times. We also discuss the implications of our results in understanding extinction events in population dynamics models expressed by means of stoichiometric relations.