Preference Cycles and Chaos

Abstract

The models of the previous parts of this book may be distinguished into those that are based on linear relationships among system components, such as the direct proportionality of the birth of fish in a lake modeled in Chapter 1, and those that capture nonlinearities, such as the per-capita grass consumption by sheep modeled in Chapter 25. The models based on linear relationships could have been solved using analytical methods. In contrast, some of the nonlinear relationships discussed in this book have no analytical solutions. To solve for their behavior over time requires numerical solutions, such as the ones that we adopted here.

It could be argued that a study of very simple nonlinear difference equations . . . should be a part of high school or elementary college mathematics courses. They would enrich the intuition of students who are currently nurtured on a diet of almost exclusively linear problems.

R. May and G. Oster, “Bifurcations and Dynamic Complexity in Simple Ecological Models,” American Naturalist, 110 (1976): 573–599