arXiv subjects

Alessandra De Rossi

Publications and source records attributed to Alessandra De Rossi.

26 records · Page 2Linked to original sources

arXiv2015

Graphical representation of separatrices of attraction basins in two and three dimensional dynamical systems

In this paper we consider the problem of reconstructing separatrices in dynamical systems. In particular, here we aim at partitioning the domain approximating the boundaries of the basins of attraction of different stable equilibria. We start from the 2D case sketched in \cite{cavoretto11} and the approximation scheme presented in \cite{cavoretto11,C-D-P-V}, and then we extend the reconstruction scheme of separatrices in the cases of three dimensional models with two and three stable equilibria. For this purpose we construct computational algorithms and procedures for the detection and the refinement of points located on the separatrix manifolds that partition the phase space. The use of the so-called meshfree or meshless methods is used to reconstruct the separatrices.

math.NA↗

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↗

arXiv2014

A trivariate interpolation algorithm using a cube-partition searching procedure

In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions. The partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube-partition searching procedure. More precisely, we construct a cube structure, which partitions the domain and strictly depends on the size of its subdomains, so that the new searching procedure and, accordingly, the resulting algorithm enable us to efficiently deal with a large number of nodes. Complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm.

math.NA↗

arXiv2014

Hybrid spherical approximation

In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical harmonics as local approximants. Moreover, a spherical zone algorithm is efficiently implemented, which works well also when the amount of data is very large, since it is based on an optimized searching procedure. Numerical results show good accuracy of the method, also on real geomagnetic data.

math.NA↗

arXiv2014

Local interpolation schemes for landmark-based image registration: a comparison

In this paper we focus, from a mathematical point of view, on properties and performances of some local interpolation schemes for landmark-based image registration. Precisely, we consider modified Shepard's interpolants, Wendland's functions, and Lobachevsky splines. They are quite unlike each other, but all of them are compactly supported and enjoy interesting theoretical and computational properties. In particular, we point out some unusual forms of the considered functions. Finally, detailed numerical comparisons are given, considering also Gaussians and thin plate splines, which are really globally supported but widely used in applications.

math.NA↗

arXiv2014

A food chain ecoepidemic model: infection at the bottom trophic level

In this paper we consider a three level food web subject to a disease affecting the bottom prey. The resulting dynamics is much richer with respect to the purely demographic model, in that it contains more transcritical bifurcations, gluing together the various equilibria, as well as persistent limit cycles, which are shown to be absent in the classical case. Finally, bistability is discovered among some equilibria, leading to situations in which the computation of their basins of attraction is relevant for the system outcome in terms of its biological implications.

q-bio.PE↗

arXiv2014

Two-strain ecoepidemic systems: the obligated mutualism case

We present a model for obligated mutualistic associations, in which two transmissible diseases are allowed to infect just one population. As the general model proves too hard to be fully analytically investigated, some special cases are analysed. Among our findings, the coexistence of the two strains does not appear possible, under the model assumptions. Furthermore, in particularly unfavorable circumstances the ecosystem may disappear. In this respect, an accurate computation of the basin of attraction of the origin is provided using novel techniques. For this obligated mutualistic system the presence of the diseases appears to be less relevant than in many other circumstances in ecoepidemiology, including also the case of facultative symbiotic associations.

q-bio.PE↗