Julia Sánchez Sanz
(Basque Center for Applied Mathematics, Bilbao, Spanyolország)
On the computation of the eigenvalues of the Daphnia model
In the first part of this talk I present a pseudospectral method for computing numerically the eigenvalues of linear sysyems of Volterra functional equations (VFE) coupled to delay differential equations (DDE). The method consists of defining an abstract Cauchy problem equivalent to the VFE/DDE system through the infinitesimal generator of its solution operator, then discretize it using polynomial interpolation and differentiation, and finally compute the eigenvalues of the discrete system. In the second part of the talk I will introduce the Daphnia model, which is a realistic size structured consumer-resource model, and adapt the method for the computation of its eigenvalues. The adaptation of the method to the Daphnia model is a chalange from a numerical and a computational point of view due to distributed delays, size and survival probability given implictly by the solution of external ODE and state dependent maturation. Finally, I present some results where I compare and show consistencybetween computed eigenvalues and stability boundaries from the literature.
