Chapter 2.7, Problem 1E

Interpretation Introduction

Interpretation:

To identify all equilibrium points and their stability for the vector field $\stackrel{\text{.}}{\text{x}}\text{ = x(1- x)}$. Plot the function $\text{V(x)}$.

Concept Introduction:

Potential is $\dot{\text{x}}\text{ = f(x) = -}\frac{\text{dV}}{\text{dx}}$

The points of minima in $\text{ V(x) }$ function are the stable equilibrium points, and the points of maxima are the points of unstable equilibrium.