In the previous chapters, our analysis was mostly focused on the cases when species diﬀusivity is constant. There is, however, growing evidence that in some ecological situations species motility can depend on the population density (Gurney and Nisbet, 1975; Hengeveld, 1989). There are diﬀerent manifestations of this phenomenon and diﬀerent modeling approaches to take it into account (Turchin, 1998; Ardity et al., 2001). Here we assume that densitydependence of species motility can be adequately described by means of variable diﬀusivity. Our goal is to investigate what changes density-dependent diﬀusion can bring into the system dynamics.