Partial differential equations

Abstract

Spatially homogeneous processes of change are the subject of the preceding chapter. Partial differential equations are one method to model the interplay of these processes with spatial phenomena such as movement of individuals and/or a heterogeneous environment. Random motion of organisms might be described as diffusion, and directed motion as advection. The latter can be composed of locomotion and motion of the surrounding medium. The focus of this chapter is on classical systems of no more than two interacting and diffusing populations. The potential of such systems to exhibit spatiotemporal pattern formation is studied. © 2011 Springer-Verlag Berlin Heidelberg.