The peroxidase–oxidase (PO) reaction is a paradigmatic (bio)chemical system well suited to study the organization and stability of self-sustained oscillatory phases typically present in nonlinear systems. The PO reaction can be simulated by the state-of-the-art Bronnikova–Fedkina–Schaffer–Olsen model involving ten coupled ordinary differential equations. The complex and dynamically rich distribution of self-sustained oscillatory stability phases of this model was recently investigated in detail. However, would it be possible to understand aspects of such a complex model using much simpler models? Here, we investigate stability phases predicted by three simple four-variable subnetworks derived from the complete model. While stability diagrams for such subnetworks are found to be distorted compared to those of the complete model, we find them to surprisingly preserve significant features of the original model as well as from the experimental system, e.g., period-doubling and period-adding scenarios. In addition, return maps obtained from the subnetworks look very similar to maps obtained in the experimental system under different conditions. Finally, two of the three subnetwork models are found to exhibit quint points, i.e., recently reported singular points where five distinct stability phases coalesce. We also provide experimental evidence that such quint points are present in the PO reaction.
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June 2022
Research Article|
June 10 2022
Complexity in subnetworks of a peroxidase–oxidase reaction model
Jason A. C. Gallas
;
Jason A. C. Gallas
a)
(Conceptualization, Formal analysis, Investigation, Software, Writing – original draft, Writing – review & editing)
1
Instituto de Altos Estudos da Paraíba
, Rua Silvino Lopes 419-2502, 58039-190 João Pessoa, Brazil
2
Max-Planck Institute for the Physics of Complex Systems
, Nöthnitzer Str. 38, 01187 Dresden, Germany
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Lars F. Olsen
Lars F. Olsen
b)
(Conceptualization, Formal analysis, Writing – original draft, Writing – review & editing)
3
PhyLife, Institute of Biochemistry and Molecular Biology, University of Southern Denmark
, DK-5230 Odense M, Denmark
b)Author to whom correspondence should be addressed: [email protected]
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a)
Also at: Complexity Sciences Center, 9225 Collins Avenue Suite 1208, Surfside, Florida 33154-3001, USA. Electronic mail: [email protected]
b)Author to whom correspondence should be addressed: [email protected]
Note: This article is part of the Focus Issue, From Chemical Oscillations to Applications of Nonlinear Dynamics Dedicated to Richard J. Field on the Occasion of his 80th Birthday.
Chaos 32, 063122 (2022)
Article history
Received:
March 26 2022
Accepted:
May 23 2022
Citation
Jason A. C. Gallas, Lars F. Olsen; Complexity in subnetworks of a peroxidase–oxidase reaction model. Chaos 1 June 2022; 32 (6): 063122. https://doi.org/10.1063/5.0093169
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