Spatial-temporal dynamics of a localized populational "burst" in a distributed prey-predator system

We consider the functioning of a distributed two-species prey-predator comm unity using a biologically reasonable model: the growth of the prey is gove rned by a logistic law and the grazing is described by Ivlev scheme. Origin ally, both populations are localized in a finite domain. We show that this relatively simple system possesses a very rich behavior. The invasion of bo th species typically takes place as propagation of "populational" front wav es which, depending on the problem parameters, can have rather complicated structure. The fronts may either propagate simultaneously or the wave of pr ey moves with a greater speed. After the waves have propagated, strongly;in homogeneous transient "patchy" distribution may arises. For the boundaries of the domains in parameter space correspondind to different regimes of the system, strict mathematical expressions are obtained.