# Chemical systems with limit cycles

Source: [Chemical systems with limit cycles](<https://www.sota2.com/research/paper/68fa59f71e209131ce9bbad0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T16:13:41.541Z

Authors: Radek Erban, Hye-Won Kang

Published: 2022-11-10T18:43:19.000Z

## Abstract

The dynamics of a chemical reaction network (CRN) is often modelled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of concentrations of chemical species involved. Given an arbitrarily large integer $K \\in {\\mathbb N}$, we show that there exists a CRN such that its ODE model has at least $K$ stable limit cycles. Such a CRN can be constructed with reactions of at most second order provided that the number of chemical species grows linearly with $K$. Bounds on the minimal number of chemical species and the minimal number of chemical reactions are presented for CRNs with $K$ stable limit cycles and at most second order or seventh order kinetics. We also show that CRNs with only two chemical species can have $K$ stable limit cycles, when the order of chemical reactions grows linearly with $K$.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2211.05755>)

[PDF](<https://arxiv.org/pdf/2211.05755.pdf>)