2008/10/22 by Thierry Dauxois, Francesca Di Patti, Duccio Fanelli +2 · 2 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Autocatalysis #Autocatalytic reaction #Classical mechanics #Gene Regulatory Network Analysis #Kinetics #Origins and Evolution of Life #Physics #Statistical physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.79.036112
published as Physical Review E 79, 036112 (2009) · Submitted to Phys. Rev. E
arxiv created 2008/10/22 · openalex publication_date 2009/03/24 · arxiv updated 2015/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 is 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.