ABSTRACT
This chapter increases our understanding of the cause and nature of the stability present in physical systems. The nonlinear model used here to study the role of coupling in stabilizing and synchronizing nonlinear systems is derived from population dynamics, though several of our results appear valid for general nonlinear maps. The chapter analyzes the effect of migration by studying the interactive dynamics of two subcolonies of a single species. It considers two interacting populations (colonies) of biological organisms, each of whose population dynamics is described by equations. The interaction between the colonies may be thought of as being brought about by migration between the two populations. The chapter investigates the effect of increasing the number of habitats that are coupled. It assumes that more than two habitats can be present on a ring and adjacent habitats are coupled through migration. The stabilization demonstrated is applicable to discrete dynamics in the form of maps.
