Chapter 4.3, Problem 5E

Interpretation Introduction

Interpretation:

The phase portrait of a function $\dot{\text{θ}}\text{ = μ + cosθ + cos2θ}$ with a control parameter $\text{μ}$ is to be drawn, and the bifurcation which occurs as $\text{μ}$ varies is to be classified. Also, all the bifurcation values of $\text{μ}$ are to be obtained.

Concept Introduction:

The qualitative change in the dynamics of the flow with parameters is called bifurcation, and the points at which this occurs is called the bifurcation point.

To study the stability of the dynamical systems, bifurcation is used.

In Saddle-node bifurcation mechanism, the fixed points create, collide, and destroy.