arXiv subjects

Emma Perracchione

Publications and source records attributed to Emma Perracchione.

38 records · Page 3Linked to original sources

arXiv2014

Reliable approximation of separatrix manifolds in competition models with safety niches

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.

math.NA↗

arXiv2014

Partition of Unity Interpolation on Multivariate Convex Domains

In this paper we present a new algorithm for multivariate interpolation of scattered data sets lying in convex domains $Ω\subseteq \RR^N$, for any $N \geq 2$. To organize the points in a multidimensional space, we build a $kd$-tree space-partitioning data structure, which is used to efficiently apply a partition of unity interpolant. This global scheme is combined with local radial basis function approximants and compactly supported weight functions. A detailed description of the algorithm for convex domains and a complexity analysis of the computational procedures are also considered. Several numerical experiments show the performances of the interpolation algorithm on various sets of Halton data points contained in $Ω$, where $Ω$ can be any convex domain like a 2D polygon or a 3D polyhedron.

math.NA↗