Chemical systems with limit cycles

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2211.05755.pdf (1.03 MB)

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https://arxiv.org/abs/2211.05755

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https://doi.org/10.48550/arXiv.2211.05755
 http://hdl.handle.net/11603/26457

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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2022-11-10

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journal articles
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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∈N, we show that there exists a CRN such that its ODE model has at least K stable limit cycles. In particular, we show that N(K)≤K+2, where N(K) is the minimal number of chemical species that a CRN with K limit cycles can have. Bounds on the minimal number of chemical reactions and on the minimal size of CRNs with at most second-order kinetics are also provided for CRNs with K limit cycles.