Stern-Brocot arithmetic in dynamics of a biochemical reaction model.

Abstract

A simple almost fifty year old four-variable model of the peroxidase-oxidase reaction has been studied using 2D isospike stability diagrams, 2D maximum Lyapunov exponent diagrams, and other nonlinear numerical methods. The model contains two positive feedback loops. For slightly different sets of parameters, compared to the original parameters, the model reveals a wealth of dynamic behaviors, not previously reported for this model. For example, contrary to expectations, the model is capable of reproducing all early observations of mixed-mode and bursting oscillations and chaos. Furthermore, for some parameters, the mixed-mode oscillations are organized according to Stern-Brocot arithmetic. The regions of mixed-mode oscillations are separated by narrow regions of chaotic dynamics.