Routes to Chaos in the Peroxidase−Oxidase Reaction:  Period-Doubling and Period-Adding

Abstract

Previous investigations of the peroxidase−oxidase reaction indicate the existence of a period-doubling route to chaos at pH 5.2 and a period-adding route at pH 6.3. In the present study, we extend these results in two regards: (i) The reaction was studied at a series of intermediate pH values under otherwise identical conditions. The new experiments suggest that the transition from period-doubling to period-adding takes place at approximately pH 5.4 and is characterized by a loss of dynamical complexity. (ii) A detailed model (Bronnikova, T. V.; Fed'kina, V. R.; Schaffer, W. M.; Olsen, L. F. J. Phys. Chem. 1995, 99, 9309−9312) was shown capable of reproducing the principal experimental results. These include the shift from period-doubling to period-adding, the existence of narrow regions of period-doubling between adjacent mixed-mode oscillations in the period-adding regime and changes in cycle amplitude.

Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model

“…Two progressions can be easily distinguished: Panels for 2, 3, and 4 peaks belong to the main progression, while panels for 5 and 7 peaks belong to the secondary projection. Note the growing amplitudes of the oscillations, specially B. Progressions between oscillations having 2, 5, 3 peaks were already observed experimentally in the enzyme reaction by Hauser et al 17,18 Fig. 1(c).…”

“…[6][7][8][9][10][11][12][13][14][15] The PO system has been also object of experimental investigations [16][17][18] and, for example, an experimentally determined stability diagram for the system is known in the control plane spanned by the NADH influx rate and the pH value of the medium. 18 Recently, the structural organization of this control plane was the object of a detailed numerical investigation, 19 based on a mechanism due to Bronnikova, Fedkina, Schaffer, and Olsen, 20 the so-called BFSO model. The BFSO mechanism can reproduce with good agreement most of the experimentally observed complex dynamics such as, for example, chaotic, quasi-periodic, and mixed-mode oscillations.…”

Periodic and Bursting pH Oscillations in an Enzyme Model Reaction

“…The number of such small bursts augments continuously as the flow rate increases. Such behaviour is known for mixed-mode oscillations which follow a so-called period-adding scenario [23][24][25].…”

Dynamic complexities in a single-species discrete population model with stage structure and birth pulses☆

“…Notice that if the cycles to left of a given chaotic windows are of period k, then the cycles to the right are of period k þ 1. Those so-called ''period-adding'' sequence have been observed in chemical reactions [18,20]. Period-adding is also presented in many papers [21,22], and the density-dependent age structured model studied by Guckenheimer et al [22].…”