Chapter 3.5, Problem 7E

Interpretation Introduction

Interpretation:

To find the dimensions of the system dimensional parameters $\text{r}$, $\text{K}$, ${\text{N}}_{\text{0}}$. To show that the system can be rewritten in the dimensionless form $\frac{\text{dx }}{\text{dτ}}{\text{= x(1-x), x(0) = x}}_{\text{0}}$. To find a different non-dimensionalization in terms of variable $\text{u}$ and $\text{τ}$, where $\text{u}$ is chosen with initial condition ${\text{u}}_{\text{0}}\text{= 1}$. To mention the advantages of non-dimensionalization.

Concept Introduction:

Express the equation in dimension less form.

Rewrite the equation using the initial condition.

Use dimensionless parameter to rewrite the logistic equation.

Non-dimensionalize and simplify the equation to reduce the number of parameters.