Chapter 8.2, Problem 16E

Interpretation Introduction

Interpretation:

To show that given system undergoes subcritical Hopf bifurcation by using analytical criterion.

Concept Introduction:

Fixed point of a differential equation is a point where $\text{f(x*) = 0 ; while substitution f(x*) = }\dot{\text{x}}\text{ is used and x\&*\#x00A0;is a fixed point}$

Nullclines are the curves where either $\dot{\text{x}}=0\text{ or }\dot{\text{y}}\text{ = 0}$. They show whether the flow is completely vertical or horizontal.

A subcritical Hopf bifurcationoccurs at In the case of Hopf bifurcation, when $\text{μ> 0}$, unstable cycle inside the limit cycle region shrinks to zeroand origin becomes unstable. For $\text{μ> 0}$, the large-amplitude limit cycle is the onlyattractor thatremains.