  In dynamical systems saddle points partition the domain into basins of
attractions of the remaining locally stable equilibria. This situation is
rather common especially in population dynamics models, like prey-predator or
competition systems. Focusing on squirrels population models with niche, in
this paper we design algorithms for the detection and the refinement of points
lying on the separatrix manifold partitioning the phase space. We consider both
the two populations and the three populations cases. To reconstruct the
separatrix curve and surface, we apply the Partition of Unity method, which
makes use of Wendland's functions as local approximants.
