Introduction to Chemical Oscillations Using a Modified Lotka Model

TCE

The Chemical Educator

ISSN: 1430-4171 (electronic version)

Table of Contents

Abstract Volume 5 Issue 5 (2000) pp 216-222

Introduction to Chemical Oscillations Using a Modified Lotka Model

Enrique Peacock-López

Department of Chemistry, Williams College, Williamstown, MA 01267

Published online: 24 August 2000

Abstract. In teaching chemical kinetics most textbooks use the Lotka–Volterra Model to introduce the concept of chemical oscillations. Unfortunately, the Lotka–Volterra Model yields neutrally stable limit cycles for any initial conditions, which is a nonphysical property not observed in chemical kinetics. A more physical, two-variable model with simple linear stability analysis is, therefore, desirable. Here, we consider a Modified Lotka–Volterra Model that shows multiple physical steady states and both damped and stable oscillations. We can also study a stable node bifurcation to a saddle point and a stable node bifurcation to a stable limit cycle. This dynamically richer model can be analyzed through a simple linear stability analysis and numerical integration of the system of ordinary differential equations. Both methods, in particular the analytical analysis, are accessible to undergraduate students.

Key Words: In the Classroom; physical chemistry; kinetics

(*) Corresponding author. (E-mail: epeacock@tonatiuh.williams.edu)

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