Introducing nonlinear dynamics to chemical and biochemical engineering graduate students using MATHEMATICA©

Housam Binous; Ahmed Bellagi

doi:10.1002/cae.22070

journal article Oct 28, 2018

Introducing nonlinear dynamics to chemical and biochemical engineering graduate students using MATHEMATICA©

Housam Binous

Ahmed Bellagi

Computer Applications in Engineering Education Vol. 27 No. 1 pp. 217-235 · Wiley

View at Publisher Save 10.1002/cae.22070

Abstract

AbstractIn the present paper, we present the solution of four problems drawn from the chemical and biochemical engineering field of study. These problems illustrate various important aspects of nonlinear dynamics such as limit cycles, quasi‐periodic and chaotic behaviors, time series and phase portraits, power spectra, the time‐delay reconstruction diagrams, Hopf bifurcation, bifurcation diagrams, steady state multiplicity… Among a large number of examples, we have selected the following case studies because they illustrate the basic nonlinear dynamics concepts listed previously: (i) The glycolytic oscillator model, first suggested by Sel'kov in 1968 in order to elucidate the mechanism that living cells use to obtain energy from sugar breakdown; (ii) The Oregonator model derived by Field, Körös, and Noyes in the early 1970s, which elucidates the famous oscillatory behavior observed in the Belousov–Zhabotinsky reaction; (iii) The steady state multiplicity in a biochemical reactor for both the Monod and substrate inhibition kinetics; and (iv) The three‐variable autocatalator, first proposed by Peng, Scott, and Showalter in 1990. Finally, we conclude this paper by sharing our experience teaching this subject to graduate students at King Fahd University of Petroleum & Minerals (KFUPM).

Topics

No keywords indexed for this article. Browse by subject →

References

36

[1]

10.1002/bit.260100602

[2]

Bequette B. W. (1998)

[3]

10.1126/science.1200705

[4]

10.1002/cae.20295

[5]

10.1021/ja00365a012

[6]

10.1016/0009-2509(88)85029-2

[7]

10.1109/tac.2007.914948

[8]

10.1093/oso/9780195096705.001.0001

[9]

Oscillating Chemical Reactions

Irving R. Epstein, Kenneth Kustin, Patrick De Kepper et al.

Scientific American 10.1038/scientificamerican0383-112

[10]

10.1063/1.1681288

[11]

10.1021/ja00780a001

[12]

Gray P. (1994)

[13]

Deterministic Nonperiodic Flow

Edward N. Lorenz

Journal of the Atmospheric Sciences 10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2

[14]

S.Lynch Dynamical systems with applications using Mathematica Birkhäuser Basel 2007.

[15]

10.1007/978-0-8176-4605-9

[16]

10.1007/978-3-319-06820-6_6

[17]

10.1007/978-1-4612-6374-6

[18]

10.1080/09593332508618428

[19]

10.1146/annurev.mi.03.100149.002103

[20]

10.1021/j100376a014

[21]

Prigogine I. (1980)

[22]

10.1063/1.1668896

[23]

10.1016/s0009-2509(99)00323-1

[24]

Romanovski V. G. "Dynamics of an autocatalator model" Math. Meth. Appl. Sci (2018)

[25]

10.1016/0375-9601(76)90101-8

[26]

Sandri M. "Numerical calculation of lyapunov exponents" Mathematica J (1996)

[27]

10.1007/s11144-015-0968-3

[28]

Scott S. K. (1995)

[29]

10.1016/s0009-2509(99)00314-0

[30]

10.1111/j.1432-1033.1968.tb00175.x

[31]

Strogatz S. (2014)

[32]

Thomas M. M. "The Briggs–Rauscher reaction: Chemistry clock in color" Math. Educ. Res (2006)

[33]

Tyson J. J. (1985)

[34]

10.1016/0009-2509(74)80089-8

[35]

Varma A. (1997)

[36]

10.1021/ed061p661

Metrics

13

Citations

36

References

Details

Published: Oct 28, 2018
Vol/Issue: 27(1)
Pages: 217-235
License: View

Authors

H

Housam Binous

Chemical Engineering Department King Fahd University of Petroleum and Minerals Dhahran KSA; Chemical Engineering Department National Institute of Applied Sciences and Technology University of Carthage Tunis Tunisia

A

Ahmed Bellagi

Energy Engineering Department Ecole Nationale d'Ingénieurs de Monastir—ENIM University of Monastir Monastir Tunisia

Cite This Article

Housam Binous, Ahmed Bellagi (2018). Introducing nonlinear dynamics to chemical and biochemical engineering graduate students using MATHEMATICA©. Computer Applications in Engineering Education, 27(1), 217-235. https://doi.org/10.1002/cae.22070

Introducing nonlinear dynamics to chemical and biochemical engineering graduate students using MATHEMATICA©

You May Also Like