Chapter 8.2, Problem 3E

Interpretation Introduction

Interpretation:

To plot the phase portrait for the system using computer and show that the Hopf bifurcation occurs at a $\mu =0$.

Concept Introduction:

If topological structure of the phase portrait changes by varying a parameter, then it is said that the bifurcation occurs.

For a physical system which is coming to equilibrium through exponential decay, the decay rate depends on the value of control parameter $\mu$. If by varying a parameter $\mu$, the system is coming to equilibrium slowly and becomes unstable at a critical value of control parameter ${\mu }_c$, then the system is said to have gone through supercritical Hopf bifurcation.