0000000000592514
AUTHOR
E. Venturino
An efficient method to reconstruct invariant manifolds of saddle points
In vector field analysis, saddle points have two different types of invariant manifolds, namely stable ones and unstable ones. The invariant manifolds represent separatrices that partition the domain of trajectories into invariant regions of different dynamics. In this work, we analyze the basins of attraction of two different stable nodes by reconstructing the separatrices of a saddle point. To this purpose we present a computational algorithm that detects the points lying on the manifold, considering the plane generated by the two stable eigenvectors of the saddle point. Finally we reconstruct the surface by using the moving least-squares approximant method.
Analysis of the Allee threshold via moving least square approximation
Cooperation is a common behavior between the members of predators species, because it can improve theirs skill in hunt, especially in endangered eco-systems. This behavior it is well known to induce the Strong Allee effect, that can induce the extinction when the initial populations’ is under a critical density called ”Allee threshold ”. Here we investigate the impact of the pack hunting in a predator-prey system in which the predator suffers of an infectious disease with frequency and vertical transmission. The result is a three dimensional system with the predators population divided into susceptible and infected individuals. Studying the system dynamics a scenario was identified in which…