| Abstract: | A new method is proposed for the study of population dynamics in which the growth rate is impacted by population history, i.e., levels of one or more previous generations. In particular, nonlinear perturbations are incorporated into second-order difference equations, two fundamental time scales are assumed for the solution, and a differential system is generated to approximate the “slow” variation. Solutions of the approximating differential system are developed by computer simulation and the theory of nonlinear oscillations. The geometry of the phase planes describing the approximate “slow” variation is represented graphically and the interaction of fast and slow time scales analyzed. Relationships of the model to experimental data on small mammal populations are discussed. The experimental data was collected at the National Institute of Health under the direction of Dr. John B. Calhoun. |
