Advanced Engineering Mathematics, 7th Edition

2.8 Nonlinear Models

INTRODUCTION

We finish our discussion of single first-order differential equations by examining some nonlinear mathematical models.

Population Dynamics

If P(t) denotes the size of a population at time t, the model for exponential growth begins with the assumption that dP/dt = kP for some k > 0. In this model the relative, or specific, growth rate defined by

(1)

is assumed to be a constant k. True cases of exponential growth over long periods of time are hard to find, because the limited resources of the environment will ...