EXPLORING LIMIT CYCLES IN CHEMICAL SYSTEMS - Venkateswarlu, Velpula; Nagarani, Dharmarajula; Rambabu, D. (Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2020)
A system of ordinary differential equations (ODEs) with polynomial right-hand sides that represent the time evolution of concentrations of the chemical species involved are commonly used to model the dynamics of a chemical reaction network (CRN) under the assumption of mass action kinetics. We demonstrate that there is a CRN such that its ODE model has at least K stable limit cycles, given an arbitrarily big integer K N. If the number of chemical species increases linearly with K, then a CRN of at most second order can be built. Limits are provided for CRNs with K stable limit cycles and at most second order or seventh order kinetics about the minimum number of chemical species and the minimum number of chemical reactions. Additionally, we demonstrate that when the order of chemical reactions increases linearly with K, CRNs with just two chemical species can have K stable limit cycles.