We consider an ecosystem in which spiders may be transported by the wind from vineyards into the ... more We consider an ecosystem in which spiders may be transported by the wind from vineyards into the surrounding woods and vice versa. The model takes into account this tranport phenomenon without building space explicitly into the governing equations. The equilibria of the dynamical system are analyzed together with their stability, showing that bifurcations may occur. Then the effects of indiscriminated spraying to keep pests under control is also investigated via suitable simulations.
ABSTRACT Spatial ecoepidemic models, in which diseases affect interacting populations, are often ... more ABSTRACT Spatial ecoepidemic models, in which diseases affect interacting populations, are often explored through reaction-diffusion equations. However, cellular automata (CA) are a widely recognized tool for modelling spatial pattern formation that are broadly analagous to reaction diffusion equations, but provide greater flexibility in defining population dynamics. In this work we present a CA defined to mimic the prey–predators interactions while a pathogen is affecting, in turn, one population. We explore system equilibria, given different initial conditions and local interaction neighborhoods. Furthermore, in the various ecoepidemic systems considered we report the formation of waves and spirals: a key summary of how diseases may spread among individuals. Some inferences on the predators and infection eradication strategies are presented and supported by simulations results.
This work is focused on the processes underlying the dynamics of spatially inhomogeneous plankton... more This work is focused on the processes underlying the dynamics of spatially inhomogeneous plankton communities. We demonstrate that reaction-diffusion mathematical models are an appropriate tool for searching and understanding basic mechanisms of complex spatio-temporal plankton dynamics and fractal properties ofplanktivorous fish school walks
This work is focused on the role of diffusive interaction between separate habitats in a patchy e... more This work is focused on the role of diffusive interaction between separate habitats in a patchy environment in plankton pattern formation. We demonstrate that conceptual reaction-diffusion mathematical models constitute an appropriate tool for searching and understanding basic mechanisms of plankton pattern formation and complex spatio-temporal plankton dynamics
... On the other hand the classical model that considers epidemics in a population has been ... T... more ... On the other hand the classical model that considers epidemics in a population has been ... TheLotka-Volterra model has the drawback of exhibiting neutral type oscillations around the equilibrium point ... Eq is again a saddle, and E\ shows local neutral stability under the relaxed ...
The author has recently proposed and investigated models for the study of interacting species sub... more The author has recently proposed and investigated models for the study of interacting species subject to an additional factor, a disease spreading among one of them, that somehow affects the other one. The inadequacy of such a model comes from the basic assumption on the interacting species. It is well known that the cycles found in the Lotka-Volterra system exhibit a neutral stability, and this phenomenon is carried over to the proposed model. Here we would like to extend the study to account for population dynamics leading to carrying capacities, i.e. logistic behaviour. This corresponds to the so-called quadratic predator-prey models found in the literature. We are able to show that in some cases the trajectories are bounded, and also analyse the local stability of some equilibria.
Journal of Integral Equations and Applications, 2006
This paper is dedicated to K.E. Atkinson on the occasion of his 65th birthday ABSTRACT. Using the... more This paper is dedicated to K.E. Atkinson on the occasion of his 65th birthday ABSTRACT. Using the Goursat representation for the biharmonic function and approximate solutions of a corrected Muskhelishvili equation we construct approximate solutions for biharmonic problems in smooth domains of R 2 . It is shown that the sequence of these approximate solutions converges uniformly on each compact subset of the initial domain D. Under additional conditions it converges uniformly on D. We also provide numerical examples.
International Journal of Computer Mathematics, 2014
In dynamical systems saddle points partition the domain into basins of attractions of the remaini... more 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.
International Journal of Computer Mathematics, 2012
In this paper, we consider an ecosystem in which two disease-affected populations thrive and in w... more In this paper, we consider an ecosystem in which two disease-affected populations thrive and in which the epidemics can spread from one species to the other one by contact. The feasibility and stability conditions of the equilibria of the system are investigated analytically. The model does not possess Hopf bifurcations. Numerical simulations are performed to investigate the role of the
The model simulates the activity of three neural populations using a Lotka-Volterra predator-prey... more The model simulates the activity of three neural populations using a Lotka-Volterra predator-prey system and, based on neuro-anatomical and neuro-physiological recent findings, assumes that a functional thalamo-cortical gate should be crossed by 'queuing' thalamic signals and that a sleep promoting substance acts as a modulator. The resultant activity accounts for the sleep stage transitions. In accordance with sleep cycles timing, the model proves to be able to reproduce the clustering and randomness of those peculiar transient synchronized EEG patterns (TSEP) described in normal human sleep and supposed to be related to the dynamic building up of NREM sleep until its stabilization against perturbations.
We consider an ecosystem in which spiders may be transported by the wind from vineyards into the ... more We consider an ecosystem in which spiders may be transported by the wind from vineyards into the surrounding woods and vice versa. The model takes into account this tranport phenomenon without building space explicitly into the governing equations. The equilibria of the dynamical system are analyzed together with their stability, showing that bifurcations may occur. Then the effects of indiscriminated spraying to keep pests under control is also investigated via suitable simulations.
ABSTRACT Spatial ecoepidemic models, in which diseases affect interacting populations, are often ... more ABSTRACT Spatial ecoepidemic models, in which diseases affect interacting populations, are often explored through reaction-diffusion equations. However, cellular automata (CA) are a widely recognized tool for modelling spatial pattern formation that are broadly analagous to reaction diffusion equations, but provide greater flexibility in defining population dynamics. In this work we present a CA defined to mimic the prey–predators interactions while a pathogen is affecting, in turn, one population. We explore system equilibria, given different initial conditions and local interaction neighborhoods. Furthermore, in the various ecoepidemic systems considered we report the formation of waves and spirals: a key summary of how diseases may spread among individuals. Some inferences on the predators and infection eradication strategies are presented and supported by simulations results.
This work is focused on the processes underlying the dynamics of spatially inhomogeneous plankton... more This work is focused on the processes underlying the dynamics of spatially inhomogeneous plankton communities. We demonstrate that reaction-diffusion mathematical models are an appropriate tool for searching and understanding basic mechanisms of complex spatio-temporal plankton dynamics and fractal properties ofplanktivorous fish school walks
This work is focused on the role of diffusive interaction between separate habitats in a patchy e... more This work is focused on the role of diffusive interaction between separate habitats in a patchy environment in plankton pattern formation. We demonstrate that conceptual reaction-diffusion mathematical models constitute an appropriate tool for searching and understanding basic mechanisms of plankton pattern formation and complex spatio-temporal plankton dynamics
... On the other hand the classical model that considers epidemics in a population has been ... T... more ... On the other hand the classical model that considers epidemics in a population has been ... TheLotka-Volterra model has the drawback of exhibiting neutral type oscillations around the equilibrium point ... Eq is again a saddle, and E\ shows local neutral stability under the relaxed ...
The author has recently proposed and investigated models for the study of interacting species sub... more The author has recently proposed and investigated models for the study of interacting species subject to an additional factor, a disease spreading among one of them, that somehow affects the other one. The inadequacy of such a model comes from the basic assumption on the interacting species. It is well known that the cycles found in the Lotka-Volterra system exhibit a neutral stability, and this phenomenon is carried over to the proposed model. Here we would like to extend the study to account for population dynamics leading to carrying capacities, i.e. logistic behaviour. This corresponds to the so-called quadratic predator-prey models found in the literature. We are able to show that in some cases the trajectories are bounded, and also analyse the local stability of some equilibria.
Journal of Integral Equations and Applications, 2006
This paper is dedicated to K.E. Atkinson on the occasion of his 65th birthday ABSTRACT. Using the... more This paper is dedicated to K.E. Atkinson on the occasion of his 65th birthday ABSTRACT. Using the Goursat representation for the biharmonic function and approximate solutions of a corrected Muskhelishvili equation we construct approximate solutions for biharmonic problems in smooth domains of R 2 . It is shown that the sequence of these approximate solutions converges uniformly on each compact subset of the initial domain D. Under additional conditions it converges uniformly on D. We also provide numerical examples.
International Journal of Computer Mathematics, 2014
In dynamical systems saddle points partition the domain into basins of attractions of the remaini... more 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.
International Journal of Computer Mathematics, 2012
In this paper, we consider an ecosystem in which two disease-affected populations thrive and in w... more In this paper, we consider an ecosystem in which two disease-affected populations thrive and in which the epidemics can spread from one species to the other one by contact. The feasibility and stability conditions of the equilibria of the system are investigated analytically. The model does not possess Hopf bifurcations. Numerical simulations are performed to investigate the role of the
The model simulates the activity of three neural populations using a Lotka-Volterra predator-prey... more The model simulates the activity of three neural populations using a Lotka-Volterra predator-prey system and, based on neuro-anatomical and neuro-physiological recent findings, assumes that a functional thalamo-cortical gate should be crossed by 'queuing' thalamic signals and that a sleep promoting substance acts as a modulator. The resultant activity accounts for the sleep stage transitions. In accordance with sleep cycles timing, the model proves to be able to reproduce the clustering and randomness of those peculiar transient synchronized EEG patterns (TSEP) described in normal human sleep and supposed to be related to the dynamic building up of NREM sleep until its stabilization against perturbations.
Uploads
Papers by E. Venturino