Enhanced stochastic oscillations in autocatalytic reactions

TL;DR

This paper investigates how stochastic fluctuations induce enhanced oscillations in autocatalytic chemical reactions, revealing resonance effects and analyzing power spectra for different system sizes and complexities.

Contribution

It demonstrates that intrinsic noise can cause amplified oscillations in autocatalytic reactions and provides a detailed comparison between theoretical predictions and simulations for systems with varying numbers of constituents.

Findings

Stochastic fluctuations induce regular oscillations with enhanced amplitude.

Power spectra show distinct forms depending on the number of chemical constituents.

Good agreement between theory and simulations, especially for systems with 8 constituents.

Abstract

We study a simplified scheme of $k$ coupled autocatalytic reactions, previously introduced by Togashi and Kaneko. The role of stochastic fluctuations is elucidated through the use of the van Kampen system-size expansion and the results compared with direct stochastic simulations. Regular temporal oscillations are predicted to occur for the concentration of the various chemical constituents, with an enhanced amplitude resulting from a resonance which is induced by the intrinsic graininess of the system. The associated power spectra are determined and have a different form depending on the number of chemical constituents, $k$. We make detailed comparisons in the two cases $k=4$ and $k=8$. Agreement between the theoretical and numerical results for the power spectrum are good in both cases. The resulting spectrum is especially interesting in the $k=8$ system, since it has two peaks, which the system-size expansion is still able to reproduce accurately.