2025/11/14 by Jérémie Unterberger, Unterberger, Jeremie · 1 citation
Physics and Astronomy · Biochemistry, Genetics and Molecular Biology · #Origins and Evolution of Life #Gene Regulatory Network Analysis #Advanced Thermodynamics and Statistical Mechanics
paper · pdf · doi:10.48550/arxiv.2511.11073
Autocatalytic chemical reaction networks are dynamical systems whose linearization around zero, dX/dt = AX, is represented by a Perron-Frobenius matrix A with positive Lyapunov exponent; this exponent gives the growth rate of the species concentration vector X in the diluted regime, i.e. in a vicinity of zero. We introduce here a new, general recursive procedure providing precise quantitative information about Lyapunov data, namely, the Lyapunov eigenvalue, and left and right eigenvectors. Our estimates are based on a multi-scale algorithm inspired from Wilson's renormalization group method in quantum field theory, and Markov chain arguments introduced in (Nghe & Unterberger). They are compatible with the very scarce knowledge of kinetic rates (coefficients of A) generally available in chemistry, and take on the form of simple rational functions of the latter.