Chapter 6.4, Problem 3E

Interpretation Introduction

Interpretation:

To find the fixed points for $\dot{\text{x}}\text{ = x (3 - 2x - 2y)}$ and $\dot{\text{y}}\text{ = y (2 - x - y)}$ also investigate their stability, draw the nullclines, and sketch plausible phase portraits. Indicate the basins of attraction of any stable points.

Concept Introduction:

Fixed points of the system are the points where $\dot{\text{x}}\text{ = 0}$, $\dot{\text{y}}\text{ = 0}\text{.}$

$\text{x -}$ nullclines are a set of points in the phase plane where $\frac{\text{dx}}{\text{dt}}\text{ = 0}$. At these points where the vectors are either upward or downward.

$\text{y -}$ nullclines is a set of points where $\frac{\text{dy}}{\text{dt}}\text{ = 0}$. These are the points where vectors are in horizontal direction.