Chapter 8.2, Problem 11E

Interpretation Introduction

Interpretation:

For the given system equation $\ddot{\text{x}}\text{ + }\mu {\dot{\text{x}}\text{ + x - x}}^3\text{= 0 }$, show that the origin changes from a stable to an unstable spiral as $\mu$ decreases to zero. Plot the phase portraits for $\mu >0$, $\mu =0$, and $\mu <0$, and show that the bifurcation at $\mu =0$ is a degenerative version of the bifurcation.

Concept Introduction:

Determine the fixed point for the given system.

Determine the bifurcation using the Jacobian matrix and fixed point.

Sketch phase portrait using system equation.