Chapter 6.4, Problem 5E

Interpretation Introduction

Interpretation:

To nondimensionalize and analyze the given model ${\dot{\text{N}}}_{\text{1}}{\text{ = r}}_{\text{1}}{\text{N}}_{\text{1}}\left(\text{1 - }\frac{{\text{N}}_{\text{1}}}{{\text{K}}_{\text{1}}}\right){\text{ - b}}_{\text{1}}{\text{N}}_{\text{1}}{\text{N}}_{\text{2}}$, ${\dot{\text{N}}}_{\text{2}}{\text{ = r}}_2{\text{N}}_{\text{2}}{\text{ - b}}_{\text{2}}{\text{N}}_{\text{1}}{\text{N}}_{\text{2}}$. To show that there are qualitatively different kinds of phase portrait depending on the size of ${\text{K}}_{\text{1}}$. To describe the long-term behavior in each case.

Concept Introduction:

The dimensionless equations can be found by substituting different parameters in the given model.

Nullclines are the curves in the phase portrait where either $\dot{\text{x}}\text{ = 0}$ or $\dot{\text{y}}\text{ = 0}$.