Complex dynamics in an unexplored simple model of the peroxidase–oxidase reaction.

This article focuses on a detailed numerical study of a previously neglected version of the Olsen model of the peroxidase–oxidase (PO) reaction, a prototypical biochemical system exhibiting complex nonlinear dynamics. Using two-dimensional isospike stability diagrams and maximum Lyapunov exponent analyses, the study reveals that this model (with stoichiometric coefficient \( n=2 \)) displays a rich variety of dynamic behaviors—including mixed-mode oscillations, bursting, quasiperiodicity, and chaotic dynamics—similar yet distinct from the more studied Olsen model with \( n=3 \). Both models exhibit complex bifurcation structures with coexistence of multiple periodic and non-periodic attractors, and transitions from quasiperiodic to chaotic oscillations occur via wrinkling and fractalization of tori. The findings suggest that such complex dynamic landscapes in simple biochemical models may provide insights into biological signaling processes, such as intracellular calcium oscillations, by illustrating how small parameter changes can induce transitions between diverse dynamic states.