Chapter 8.4, Problem 3E

Interpretation Introduction

Interpretation:

To find the value of $\text{μ}$ by using numerical integration at which homoclinic bifurcation occurs, and to sketch the phase portrait of the system just above and below that $\text{μ}$.

Concept Introduction:

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

Holonomic bifurcation is the infinite period bifurcation in which limit cycle moves closer and closer to the saddle point, and at the bifurcation, cycle touches the saddle point and becomes a holonomic orbit.

Phase portraits represent the trajectories of the system with respect to the parameters and give a qualitative idea about the evolution of the system, its fixed points, whether they will attract or repel the flow, etc.