Chemical Oscillations out of Chemical Noise

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 1 arXiv:1004.2722v2 [cond-mat.stat-mech] 2 Oct 2011 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.