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

In 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).