Chapter 3.4, Problem 12E

Interpretation Introduction

Interpretation:

An example of quad-furcation is to be constructed. We pointed out that the pitchfork bifurcation could be called a trifurcation since three branches of fixed points appear for $\text{r > 0}$.

Concept Introduction:

Bifurcation theory is used to study the stability of the dynamical systems.

Fixed points are the points where, $\dot{\text{x}}\text{ = 0}$.

The phenomenon in which fixed points are created and destroyed by varying the control parameter is termed as saddle-node bifurcation.