The inheritance of local bifurcations in mass action networks

2023/12/20 by Murad Banaji, Banaji, Murad, Balázs Boros +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #34C23 #34D15 #80A30 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #Slime Mold and Myxomycetes Research

paper · doi:10.48550/arxiv.2312.12897

openalex publication_date 2023/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider local bifurcations of equilibria in dynamical systems arising from chemical reaction networks with mass action kinetics. In particular, given any mass action network admitting a local bifurcation of equilibria, assuming only a general transversality condition, we list some enlargements of the network which preserve its capacity for the bifurcation. These results allow us to identify bifurcations in reaction networks from examination of their subnetworks, extending and complementing previous results on the inheritance of nontrivial dynamical behaviours amongst mass action networks. A number of examples are presented to illustrate applicability of the results.

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