Routes to chaos in the peroxidase-oxidase reaction. 2. The fat torus scenario

Tatiana V. Bronnikova, William M Schaffer, Marcus J B Hauser, Lars F. Olsen

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Abstract

Experimental studies [Hauser, M. J. B.; Olsen, L. F. J. Chem. Soc., Faraday Trans. 1996, 92, 2857-2863] of the peroxidase-oxidase (PO) reaction at pH values in excess of 5.4 suggest the existence of narrow regions of complex dynamics between adjacent mixed-mode oscillations (MMOs) that occur in period-adding sequences. Previously [Hauser, M. J. B.; Olsen, L. F.; Bronnikova, T. V.; Schaffer, W. M. J. Phys. Chem. B 1997, 101, 5075-5083], it was argued that both the period-adding sequences and the transitional regions between neighboring MMOs are predictable by a detailed model of the reaction called BFSO [Bronnikova, T. V.; Fed'kina, V. R.; Schaffer, W. M.; Olsen, L. F. J. Phys. Chem. 1995, 99, 9309-9312]. In the present paper, we study the transitional regions via computer simulation. Our investigations indicate that the motion therein may be periodic, quasiperiodic, or chaotic. In greater detail, we observe a quasiperiodic route to chaos whereby period-doubled cycles give rise to doubled tori that, in turn, undergo homoclinic bifurcations to chaos. Because the latter transitions are a consequence of progressive fattening of the tori, we propose calling this scenario the "fat torus" route to chaos, and the homoclinic bifurcations "fat torus" bifurcations (FTBs). The numerical results are qualitatively consistent with the experimental findings reported to date. FTBs and the resultant period-doubled, fractal tori may provide a criterion for discriminating among alternative models of the PO reaction.

Original languageEnglish (US)
Pages (from-to)632-640
Number of pages9
JournalJournal of Physical Chemistry B
Volume102
Issue number3
StatePublished - Jan 15 1998

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oxidase
fats
Oils and fats
Chaos theory
Peroxidase
chaos
Oxidoreductases
Fats
routes
oscillations
Fractals
fractals
computerized simulation
cycles
Computer simulation

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Engineering(all)

Cite this

Routes to chaos in the peroxidase-oxidase reaction. 2. The fat torus scenario. / Bronnikova, Tatiana V.; Schaffer, William M; Hauser, Marcus J B; Olsen, Lars F.

In: Journal of Physical Chemistry B, Vol. 102, No. 3, 15.01.1998, p. 632-640.

Research output: Contribution to journalArticle

Bronnikova, Tatiana V. ; Schaffer, William M ; Hauser, Marcus J B ; Olsen, Lars F. / Routes to chaos in the peroxidase-oxidase reaction. 2. The fat torus scenario. In: Journal of Physical Chemistry B. 1998 ; Vol. 102, No. 3. pp. 632-640.
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