Minimal model for oscillatory dynamics of a nonlinear chemical reaction network

Sarang S. Nath*

*Corresponding author for this work

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Abstract

Since Bray's pioneering discovery exactly 100 years ago of the first oscillating reaction, more than 25 families of nonlinear oscillating reaction networks have been identified. The B–Z reaction network has been expanded, and complex models considering a score of chemical reactions and species have been developed. Here we look at the inverse problem and ask how the complexity of the models can be reduced. We quantify the dynamics of a minimal model by linear stability techniques and direct integration of the set of ODEs, and show that essential oscillatory and excitability features are satisfactorily captured. Reasons for the success of the minimal model are explained. Extensions of the model to fundamental chemical and biological processes are discussed, and application of the chemical reaction network to mathematically model nerve conduction is illustrated.

Original languageEnglish
Article number133503
JournalPhysica D: Nonlinear Phenomena
Volume441
Number of pages6
ISSN0167-2789
DOIs
Publication statusPublished - 2022

Keywords

  • Autocatalytic reactions
  • Chemical reaction dynamics
  • Complexity and complex systems
  • Excitable systems
  • Hodgkin–Huxley equations of nerve conduction
  • Stability analysis

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