Population growth modeling with boom and bust patterns: the impulsive differential equation formalism

Abstract

This note gives an overview on basic mathematical models describing the population dynamics of a single species whose vital dynamics has different time scales. We present five cases combining two time-scales with Malthusian growth in at least one scale. The dynamical behavior shows a progressive complexity, from "naive" to chaotic dynamics (in the Li-Yorke's sense). In addition, some open problems and new results are presented.