AbstractIncreasing computational power in the last decade has led to a breakthrough in the understanding of nonlinear dynamic systems. Deterministic chaos, a distinct mode of behavior qualitatively different from linear modes, can arise in systems with instabilities constrained by nonlinearities.This article overviews this new field. It is observed that deterministic chaos is associated with the presence of a basic instability, often associated with a negative loop with high‐gain and significant delay, that allows small random fluctuations to be amplified and eventually dominate the behavior of the system.The mathematical tools of qualitative analysis of nonlinear systems are applied to familiar models of urban dynamics. Spatial disaggregation in an urban migration model is shown to yield a route to chaos through period‐doubling. Alternative routes to chaos are discussed. Examples from the natural and social sciences are used to demonstrate the applicability of the tools and the ubiquity of such complex nonlinear dynamic phenom