Asymptotically stable states of non-linear age-structured monocyclic population model II. Numerical simulation

This paper is devoted to the study of evolutionary dynamics of monocyclic age-structured population including the effect of non-linear mortality (population growth feedback) and proliferation. For this purpose we developed the explicit conservative two layer difference schemes for the initial-boundary value problems for the semi-linear transport equations with non-local boundary condition for two different types of non-linear death rate. For the obtained schemes we formulate sufficient conditions for the existence of bounded numerical solutions. We then perform numerical simulations to analyse various qualitative dynamical properties of the systems. For the both considered death rates and stationary model parameters (coefficients of equations) population density is always attracted for a long time to some asymptotically stable state. We indicated in these experiments that each regime of population dynamics belongs to one of the three possible regimes: quasi-equilibrium, increasing and decreasing regimes relative to the behaviour of the maximum value by age of population density. Obtained numerical solutions show very good connection and correlation with the analytical travelling wave ones for the considered systems.