We consider a single species population obeying a saturated growth model with spatial diffusion taken into account explicitly. Strong spatial heterogeneity is considered, represented by a position dependent reproduction rate. The geometry of the problem is that of two patches where the...

In a recent model of growth developed by Lucas (Lucas, R., 2009. Ideas and growth. Economica 76, 1–19), a continuum of people interact in a random manner and copy each other’s productive ideas when it is economically beneficial to do so. This paper extends the Lucas model by assuming that...