Limit Cycles of the Schnakenberg Chemical Reaction Model

Abstract

Dynamical systems contribute to the mathematical modeling of chemical reactions of biological or ecological phenomena producing limit cycle oscillations. In this study, we present a computational approach to examine the bifurcations of limit cycles of the two-dimensional simple chemical reaction model known as the Schnakenberg model. With our approach, we obtain conditions on parameters of the system of the chemical reaction model which gives Hopf bifurcation. Using the Lyapunov function we show the stability of Hopf bifurcation. We illustrate the results with a numerical example.