| Autor: |
Erban, Radek, Kang, Hye-Won |
| Rok vydání: |
2022 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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 $K$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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