Chapter 8.2, Problem 2E

Interpretation Introduction

Interpretation:

To show that the given system has pure imaginary Eigenvalues at the origin when $\text{μ = 0}$.

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.

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