Non-ideal reaction-diffusion systems: Multiple routes to instability

Timur Aslyamov, Francesco Avanzini, Étienne Fodor, Massimiliano Esposito

Published 2023-04-13Version 1

We develop a general classification of the nature of the instabilities yielding spatial organization in open non-ideal reaction-diffusion systems. This encompasses dynamics where chemical species diffuse, interact with each other, and undergo chemical reactions driven out-of-equilibrium by external chemostats. We find analytically that these instabilities can be of two types: instabilities caused by molecular interactions (Cahn-Hilliard type), and instabilities caused by multimolecular out-of-equilibrium chemical reactions (Turing type). Furthermore, we identify a class of chemical reaction networks, extending beyond unimolecular networks, that can only undergo Cahn-Hilliard instabilities. We illustrate our analytical findings with numerical simulations on two reaction-diffusion models, each displaying one of the two types of instability.