Chapter 8.1, Problem 9E

Interpretation Introduction

Interpretation:

To plot the stability diagram for the system ${\ddot{\text{x}}\text{ + b}\dot{\text{x}}\text{ - kx + x}}^{\text{3}}\text{ = 0}$ where $\text{b}$ and $\text{k}$ can be positive, negative or zero. Label the bifurcation curve in $\left(\text{b, k}\right)$ plane.

Concept Introduction:

• Determine the fixed points of the system.

• Using Jacobian matrix, determine the stability of the system at the fixed points.

• Plot the bifurcation curve in $\left(\text{b, k}\right)$ plane.