### Abstract

Experimental time series of [O_{2}] generated by the peroxidase-oxidase reaction were analyzed using various methods from nonlinear dynamics. The following results were obtained: (1) Aperiodic time series are chaotic as evidenced by (i) the observation of period doubling bifurcations in response to increasing the amount of 2,4-dichlorophenol in the reaction mixture, (ii) well-defined next amplitude maps, (iii) positive Lyapunov exponents corresponding to about 0.5 bits per orbital excursion, and (iv) fractal dimensions ranging from 2.6 to 2.8. Prediction profiles obtained by subjecting the data to nonlinear forecasting give further evidence of deterministic chaos. (2) The chaotic data are nonuniform, since none of the above-mentioned methods work well when applied to the continuous data. Instead, one has to use a series of maxima. (3) Conclusions 1 and 2 are supported by the fact that similar results obtain for chaotic time series generated by a simple model of the reaction.

Original language | English (US) |
---|---|

Pages (from-to) | 8431-8441 |

Number of pages | 11 |

Journal | Journal of Physical Chemistry |

Volume | 97 |

Issue number | 32 |

State | Published - 1993 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry*,

*97*(32), 8431-8441.

**Nonlinear analyses of periodic and chaotic time series from the peroxidase-oxidase reaction.** / Geest, Torben; Olsen, Lars F.; Steinmetz, Curtis G.; Larter, Raima; Schaffer, William M.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry*, vol. 97, no. 32, pp. 8431-8441.

}

TY - JOUR

T1 - Nonlinear analyses of periodic and chaotic time series from the peroxidase-oxidase reaction

AU - Geest, Torben

AU - Olsen, Lars F.

AU - Steinmetz, Curtis G.

AU - Larter, Raima

AU - Schaffer, William M

PY - 1993

Y1 - 1993

N2 - Experimental time series of [O2] generated by the peroxidase-oxidase reaction were analyzed using various methods from nonlinear dynamics. The following results were obtained: (1) Aperiodic time series are chaotic as evidenced by (i) the observation of period doubling bifurcations in response to increasing the amount of 2,4-dichlorophenol in the reaction mixture, (ii) well-defined next amplitude maps, (iii) positive Lyapunov exponents corresponding to about 0.5 bits per orbital excursion, and (iv) fractal dimensions ranging from 2.6 to 2.8. Prediction profiles obtained by subjecting the data to nonlinear forecasting give further evidence of deterministic chaos. (2) The chaotic data are nonuniform, since none of the above-mentioned methods work well when applied to the continuous data. Instead, one has to use a series of maxima. (3) Conclusions 1 and 2 are supported by the fact that similar results obtain for chaotic time series generated by a simple model of the reaction.

AB - Experimental time series of [O2] generated by the peroxidase-oxidase reaction were analyzed using various methods from nonlinear dynamics. The following results were obtained: (1) Aperiodic time series are chaotic as evidenced by (i) the observation of period doubling bifurcations in response to increasing the amount of 2,4-dichlorophenol in the reaction mixture, (ii) well-defined next amplitude maps, (iii) positive Lyapunov exponents corresponding to about 0.5 bits per orbital excursion, and (iv) fractal dimensions ranging from 2.6 to 2.8. Prediction profiles obtained by subjecting the data to nonlinear forecasting give further evidence of deterministic chaos. (2) The chaotic data are nonuniform, since none of the above-mentioned methods work well when applied to the continuous data. Instead, one has to use a series of maxima. (3) Conclusions 1 and 2 are supported by the fact that similar results obtain for chaotic time series generated by a simple model of the reaction.

UR - http://www.scopus.com/inward/record.url?scp=0000082471&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000082471&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000082471

VL - 97

SP - 8431

EP - 8441

JO - Journal of Physical Chemistry

JF - Journal of Physical Chemistry

SN - 0022-3654

IS - 32

ER -