Chapter 2.3, Problem 4E

Interpretation Introduction

Interpretation:

Show that $\frac{\dot{\text{N}}}{\text{N}}{\text{= r - a ( N - b )}}^{\text{2}}$ provides an example of the Allee effect, if r, a and b satisfy certain constraints, to be determined.

Finding all the fixed points of the system, and classify their stability.

Sketch the solutions $\text{N (t)}$ for different initial conditions.

Comparison of the solution of the given system, and the logistic equation and their differences.

Concept Introduction:

For maximum ${\text{f}}^{″}\text{ (N) < 0 and }{\text{f}}^{\prime }\text{ (N) = 0 }\text{.}$

Fixed points are the points where $\dot{\text{N}}\text{ = 0}$.

Species growth rate equation is $\dot{\text{N}}\text{ = N f(N) = g(N)}$.