Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 85, Issue 8, Pages -Publisher
SPRINGER
DOI: 10.1007/s11538-023-01170-3
Keywords
Chemical reaction networks; Limit cycles; Mass action kinetics
Categories
Ask authors/readers for more resources
This paper investigates chemical reaction networks with multiple stable limit cycles and presents bounds on the minimal number of chemical species and reactions required.
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available