Approximation of basins of attraction for bistable dynamical system for olive disease control

Abstract

In this paper the bistability of a mathematical model for the control of an olive tree disease is studied. The basin of stability values were computed for three different pairs of bistable equilibrium points by using the software bSTAB. Moreover an extension of the software functionalities is made, first by approximating the shape of the attractors in three dimensions and second by extending the sensitivity study with respect to some important parameters of the numerical scheme, e.g. hyperparameters, to the two dimensional case. Analogously, the bifurcation diagram of the basin of stability values with respect to one parameter of the model was extended to the two dimensional case where two parameters of the model can vary simultaneously. Finally an approximation of the surfaces of the sensitivity analysis and bifurcation diagrams were made.