Period-doubling bifurcations and chaos in an enzyme reaction

Geest, Torben; Steinmetz, Curtis G.; Larter, Raima; Olsen, Lars Folke

doi:10.1021/j100193a004

Cited by 72 publications

(90 citation statements)

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“…9 These behaviors have all been observed in vitro under well controlled laboratory conditions. The PO reaction also occurs in viuo,I0 and its detailed study therefore has significant implications for understanding the role of low dimensional complex dynamics in biological systems.…”

Section: Introductionmentioning

confidence: 81%

Universality in the peroxidase-oxidase reaction: period doublings, chaos, period three, and unstable limit cycles

Steinmetz¹,

Geest²,

Larter³

1993

J. Phys. Chem.

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Recently we reported on a period doubling route to chaos in the peroxidase-oxidase (PO) reaction. This was the first report of a universal route to chaos in the PO reaction. Here we present further evidence of universality in the transition to chaos in the PO reaction. We have observed period three oscillations under conditions near where chaotic oscillations are found, and we have found that chaotic oscillations in this reaction contain unstable periodic orbits. We also report numerical results from a simple model of the PO reaction. These theoretical calculations qualitatively reproduce the spectrum of behaviors observed in this reaction.

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Section: Introductionmentioning

confidence: 81%

Universality in the peroxidase-oxidase reaction: period doublings, chaos, period three, and unstable limit cycles

Steinmetz¹,

Geest²,

Larter³

1993

J. Phys. Chem.

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“…That is, the periodic motions with high periods of the clean system are replaced by chaoslike motions when there is noise. Indeed, when a period-doubling cascade is observed in experimental situations, such as in fluid flows [5], semiconductor lasers [6], chemical reactions [7], and biological systems [8], and in a plasma reactor [9], only the first few period-doubling bifurcations can be observed.…”

mentioning

confidence: 99%

When Can Noise Induce Chaos?

1999

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Crutchfield et al. observed that noise truncates period-doubling cascade and induces chaos. To date, however, very little low-dimensional chaos has been unambiguously identified experimentally. This discrepancy stimulates us to reexamine the noisy logistic map. We find that noise can indeed induce chaos. However, this is not associated with the main 2 n cascade. We identify three basic conditions for noise to induce chaos. We also show that when noise induces chaos the complete period-doubling cascade is inhibited, otherwise the cascade is simply masked by noise. [S0031-9007(99)

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“…It is now clear that PO reactions shows a wide spectrum of interesting behaviors including simple oscillations, bistability, quasiperiodicity and chaos [7]. These behavior have all been observed in vitro under well controlled laboratory conditions.…”

Section: B Dynamical System a Descriptionmentioning

confidence: 92%

Applications of recurrence quantified analysis to study the dynamics of chaotic chemical reaction

Castellini

Romanelli

2004

Physica A: Statistical Mechanics and its Applications

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Recurrence plot is a quite easy tool to be used in time series analysis,in particular for measuring unstable periodic orbits embedded in a chaotic dynamical system. Recurrence quantified analysis (RQA) is an advance tool that allows the study of intrinsic complexity of dynamical system with a set of few parameters. We use RQA for measuring chaotic transitions of NADH chemical reaction and determine numerically its characteristic parameters such as: Correlation integral, information entropy, Maximal Lyapunov's exponent, etc. For this work we have developed command sets with performance better than TISEAN package

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Period-doubling bifurcations and chaos in an enzyme reaction

Cited by 72 publications

References 1 publication

Universality in the peroxidase-oxidase reaction: period doublings, chaos, period three, and unstable limit cycles

Universality in the peroxidase-oxidase reaction: period doublings, chaos, period three, and unstable limit cycles

When Can Noise Induce Chaos?

Applications of recurrence quantified analysis to study the dynamics of chaotic chemical reaction

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