Nonlinear Dynamics and Chaos in Insect Populations

Recent discoveries in applied mathematics have uncovered a fascinating and unexpected dynamic richness underlying even very simple nonlinear mathe­ matical models. The complexity of solutions to nonlinear equations led researchers to coin a new mathematical term, chaos, to describe the resulting behavior. This term captures the notion that in spite of the fact that these equations are purely deterministic, the resulting dynamics appear very much like a bounded random process. A surprising aspect of this discovery is the way in which it has captured the imagination of the public, becoming the subject of a New York Times best seller (30) and of a Nova television special. The popular interest in chaos emerges at least in part from the fact that solution sets are often represented as fractals, which result in complex and strangely beautiful geometric patterns. Although the subject of chaos has its lighter side, it has also formed the basis of a serious scientific revolution. Since the acciden tal discovery of chaos in a simple atmospheric weather model by Edward Lorenz in 1963 (59), chaotic dynamics have been found to