Journal article
Chemical systems with limit cycles
- Abstract:
- The dynamics of a chemical reaction network (CRN) is often modeled 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. 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.1MB, Terms of use)
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- Publisher copy:
- 10.1007/s11538-023-01170-3
Authors
- Publisher:
- Springer Nature
- Journal:
- Bulletin of Mathematical Biology More from this journal
- Volume:
- 85
- Article number:
- 76
- Publication date:
- 2023-07-04
- Acceptance date:
- 2023-05-19
- DOI:
- EISSN:
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1522-9602
- ISSN:
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0092-8240
- Language:
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English
- Keywords:
- Pubs id:
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1343492
- Local pid:
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pubs:1343492
- Deposit date:
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2023-05-21
- ARK identifier:
Terms of use
- Copyright holder:
- Erban and Kang
- Copyright date:
- 2023
- Rights statement:
- ©2023 The Author(s). Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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