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We have investigated in detail the transition from stable steady state to chaos in the DOP model of the peroxidase–oxidase reaction. Two consecutive Hopf bifurcations give rise to toroidal oscillations. Chaotic oscillations occur after the circle map associated with the torus becomes noninvertible. The supercritical region of parameter space is characterized by a periodic-chaotic sequence in which the periodic states form severely, but systematically, pruned Farey trees. In terms of both the transition to chaos and the periodic-chaotic sequence, the DOP model appears to share important qualitative characteristics with a variety of oscillating chemical reaction systems and their models.
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Steinmetz et al. (1991) studied this question.
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