Chapter 6.1, Problem 7E

Interpretation Introduction

Interpretation:

The nullcline and stable manifold for ${\dot{\text{x}}\text{ = x + e}}^{\text{-y}}$, $\dot{\text{y}}\text{ = -y}$ are to be sketched on the same phase portrait.

Concept Introduction:

Nullclines are the curve where either $\dot{\text{x}}\text{ = 0}$ or $\dot{\text{y}}\text{ = 0}\text{.}$

The x-nullclines is a set of points in the phase plane which satisfy $\dot{\text{x}}\text{ = 0}$. This represents that the flow it purely vertical. The vectors are either straight up or straight down at these points.

The y-nullclines is a set of points in the phase plane which satisfy $\dot{\text{y}}\text{ = 0}\text{.}$ This represents that the flow it purely horizontal and the vectorsarepurely horizontal at these points.