Chapter 3.1, Problem 5E

Interpretation Introduction

Interpretation:

The assumption $\text{a =}{\frac{\text{df}}{\text{dr}}|}_{{\text{(x*,r}}_{\text{c}}\text{)}}\text{=0}$ is made. It is to be verified by using equations such that $\text{a =}{\frac{\text{df}}{\text{dr}}|}_{{\text{(x*,r}}_{\text{c}}\text{)}}\ne \text{0}$

Concept Introduction:

Bifurcations and Bifurcation points - The qualitative structure of the flow can change with the parameters. In particular, fixed points can be created or destroyed, or their stability canchange qualitatively. It is called as bifurcations, and the parameter values at which these changes occurare called bifurcation points.

Saddle node bifurcation is a mechanism by which the fixed points transfer toward each other and eventually annihilate.