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Abstract

The transition from simple periodic to bursting behavior in a 3-dimensional model system of the hemin -- hydrogen peroxide -- sulfite pH oscillator is investigated. A two-parameter continuation in the flow rate and the hemin decay rate is performed to identify the region of complex dynamics. The bursting oscillations emerge subsequent to a cascade of period doubling bifurcations and the formation of a chaotic attractor in parameter space where they are found to be organized in periodic-chaotic progressions. This suggests that the bursting oscillations are not associated with phase-locked states on a 2-torus. The bursting behavior is classified by a bifurcation analysis using the intrinsic slow-fast structure of the dynamics. In particular, we find a slowly varying quasi-species (i.e. a linear combination of two species) which acts as an `internal' or quasi-static bifurcation parameter for the remaining 2-dimensional subsystem. A systematic two-parameter continuation in the internal and one of the external bifurcation parameters reveals a transition in the bursting mechanism from subHopf/fold-cycle to fold/subHopf type. In addition, the slow-fast analysis provides an explanation for the origin of quasi-periodic behavior in the hemin system, even though the underlying mechanism might be of more general importance. ©2005 The American Physical Society [accessed 2013 June 13th]