Dynamic elements of mixed-mode oscillations and chaos in a peroxidase–oxidase model network

Abstract

Three dynamic elements, DE-1, DE-2, and DE-3, are identified for the four-species Olsen model of the peroxidase–oxidase reaction. DE-1 is the damped Lotka oscillator which tends to generate smaller amplitude oscillations. DE-2 is a switch responsible for the transitions between a small and a larger amplitude oscillation. DE-3 is the reversible flux of O2 which dominates the dynamics of the full network while the concentrations of the intermediates are low. DE-1 is identified with the peroxidase catalytic cycle and DE-2 with a reaction involving compound III in the realistic mechanism. Numerical simulations on the route to chaos are presented for varying parameters affecting the three dynamic elements. Pictures of the evolution of the strange attractor that accompanies chaotic oscillations are given. As shown in the Poincaré sections of the attractor and Poincaré next-return maps, the layers of this attractor develop as even- and odd-period fixed points undergo cascades of period doubling.