13 research outputs found
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.Comment: arXiv admin note: substantial text overlap with arXiv:1404.098
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
Modeling the interactions among phythopatogens and phyllosphere microorganisms for the biological disease control of Olea europaea L.
In this paper we formulate a model for assessing the interaction between the phytopathogen Spilocaea oleaginea and the phyllosphere microorganisms that are present in the olive tree leaves. The model describes the evolution in time of the foliage of the olive tree and the two different microorganisms, the phytopathogen fungi, that negatively affect the plant causing spots in the leaves, and the beneficial phyllosphere microorganisms, that help in keeping in check the invasion of the former. The system possesses five equilibria that are suitably analysed for feasibility and stability. The model shows interesting features: a bistable behavior, exhibited by three different pairs of equilibria. The separatrix surface of the basins of attraction of one such pair is computed. This allows the possible assessment of human intervention for control of the disease. Persistent oscillations via Hopf bifurcation are also discovered.EV and IMB have been partially supported by the projects “Metodi numerici in teoria delle popolazioni” and “Metodi numerici nelle scienze applicate” of the Dipartimento di Matematica “Giuseppe Peano” of the Università di Torino. IMB has been partially supported by ”Finanziamento GNCS Giovani Ricercatori 2016”.info:eu-repo/semantics/publishedVersio
Turing Instability in an Economic-Demographic Dynamical System Can Lead to Pattern Formation on Geographical Scale
Spatial distribution of the human population is distinctly heterogeneous,
e.g. showing significant difference in the population density between urban and
rural areas. In the historical perspective, i.e. on the timescale of centuries,
the emergence of the densely populated areas at their present locations is
widely believed to be linked to more favourable environmental and climatic
conditions. In this paper, we challenge this point of view. We first identify a
few areas at different parts of the world where the environmental conditions
(quantified by the temperature, precipitation and elevation) are approximately
uniform over thousands of miles. We then examine the population distribution
across those areas to show that, in spite of the homogeneity of the
environment, it exhibits a clear nearly-periodic spatial pattern. Based on this
apparent disagreement, we hypothesize that there exists an inherent mechanism
that can lead to pattern formation even in a uniform environment. We consider a
mathematical model of the coupled demographic-economic dynamics and show that
its spatially uniform, locally stable steady state can give rise to a periodic
spatial pattern due to the Turing instability. Using computer simulations, we
show that, interestingly, the emergence of the Turing patterns eventually leads
to the system collapse.Comment: 26 pages, 14 figure