Secondary quasiperiodicity in the peroxidase–oxidase reaction

Abstract

Secondary quasiperiodicity (period-doubled oscillations modulated by an incommensurate frequency), or “Q2”, is the temporal manifestation of quasiperiodic motion on period-doubled tori. The existence of this regime in a chemical reaction was first predicted (T. V. Bronnikova, W. M. Schaffer and L. F. Olsen, J. Chem. Phys., 1996, 105, 10 849) in the course of numerical explorations of a detailed model of the peroxidase–oxidase system. Subsequent analysis (T. V. Bronnikova, W. M. Schaffer, M. J. B. Hauser and L. F. Olsen, J. Phys. Chem. B, 1998, 102, 632) suggested the possibility of homoclinic transitions (“fat torus” bifurcation) to chaos involving Q2. In the present paper, we present the first experimental evidence for secondary quasiperiodicity and fat torus bifurcations in a chemical oscillator. We also identify a second (“thin torus”) route to chaos involving Q2. The relationship of these two bifurcation scenarios to each other and to the experimental findings is discussed.