EBK NONLINEAR DYNAMICS AND CHAOS WITH S
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Chapter 2.3, Problem 5E
Interpretation Introduction

Interpretation:

x(t) increases monotonically and approaches 1 as t is to be shown by solving for X(t) and Y(t) and also by deriving a differential equation for x(t).

Concept Introduction:

The model which describes population growth of organisms is N˙ = rN ,where  N(t) is population at time t and r is growth rate.

The more accurate model is given by Verhulst, known as the logistic model, which postulates that the relative growth rate N˙N decreases linearly with N. The corresponding logistic equation is

N˙ = rN (1NK)

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