Chapter 8.1, Problem 6E

Interpretation Introduction

Interpretation:

Consider the system ${\dot{\text{x}}\text{ = y- 2x, }\dot{\text{y}}\text{ = μ + x}}^{\text{2}}\text{- y}$

Sketch the nullclines.

The bifurcations that occur as $\text{μ}$ varies is to be found and classified.

The phase portrait as a function of $\text{μ}$ is to be sketched.

Concept Introduction:

Geometrically, the x-nullclines are a set of points in the phase plane where vectors are going up or down. Algebraically, they can be found by using $\text{f(x,y) = 0}$.

Geometrically, the y-nullclines are a set of points in the phase plane where vectors are horizontal, going either left or to the right.