Chapter 7.4, Problem 2E

Interpretation Introduction

Interpretation:

For the equation $\ddot{\text{x}}\text{ + }\mu {\text{(x}}^4\text{-1)}\dot{\text{x}}\text{ + x = 0 }$, prove that the system has a unique stable limit cycle if $\mu >0$. Plot thephase portraitfor $\mu =0$. If $\mu <0$ does the system still have a limit cycle. If so, is it stable or unstable.

Concept Introduction:

UseLíénard’s Theorem and verify all the conditions for $\text{f(x)}$ and $\text{g(x)}$.

Sketch phase portrait using system equation.