On some properties of the system of differential equations with a delayed parameter

Anna Poskrobko, Antoni Leon Dawidowicz

The presentation deals with the description of a multispecies model with a delayed parameter, based on the Gurtin and MacCamy one. There is considered mutual influence of n populations under the assumption that each population develop with different dynamics, however impacting on each other. The existence and uniqueness of the solution for the new problem of the dynamics of n populations are proved, as well as the asymptotical stability of the equilibrium age distribution. We present also some additional properties of the new model of the dynamics of the ecosystem.