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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3. Consider the following theorem: Theorem: If n is an odd integer, then n³ is an odd integer. Note: There is an implicit universal quantifier for this theorem. Technically we could write: For all integers n, if n is an odd integer, then n³ is an odd integer. (a) Explore the statement by constructing at least three examples that satisfy the hypothesis, one of which uses a negative value. Verify the conclusion is true for each example. You do not need to write your examples formally, but your work should be easy to follow. (b) Pick one of your examples from part (a) and complete the following sentence frame: One example that verifies the theorem is when n = We see the hypothesis is true because and the conclusion is true because (c) Use the definition of odd to construct a know-show table that outlines the proof of the theorem. You do not need to write a proof at this time.
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