Chapter 8.3, Problem 3E

Interpretation Introduction

Interpretation:

To analyze the model for the chlorine dioxide-iodine-malonic acid oscillator for the system equations $\dot{\text{x}}\text{ = a - x - }\frac{\text{4xy}}{{\text{1+x}}^{\text{2}}}$, $\dot{\text{y}}\text{ = bx}\left(\text{1 - }\frac{\text{y}}{{\text{1+x}}^{\text{2}}}\right)$ in the limit $\text{b << 1}$. Also, sketch the limit cycle in the phase plane and estimate its period.

Concept Introduction:

Chemical oscillator is an experimental type of the Hopf bifurcation in which the system is remarkable both for its spectacular behaviour and for the story behind its discovery.

If $\text{a > 0}$, then bifurcation is subcritical.

If $\text{a < 0}$, then bifurcation is supercritical.