Chaos via mixed-mode oscillations

Abstract

The route by which chaos arises from mixed-mode periodic states in a model of the peroxidase enzyme catalysed oxidation of NADH is described. The specific model studied displays a rich variety of exotic dynamical behaviour including simple oscillations, quasiperiodicity, bistability between periodic states, complex periodic oscillations (including the mixed-mode type) and chaos. The route to chaos in this system involves a torus attractor which becomes destabilized and breaks up into a fractal object, a strange attractor. The mixed-mode states correspond to phase-locking on this fractal attractor and are arranged in staircases according to the complexity of the state. In this paper, we investigate the sequence leading from a mixed-mode periodic state to a chaotic one in the staircase region and find a familiar cascade of period-doubling bifurcations, which finally culminate in chaos.