In this paper we study the nonlinear age-structured model of a polycyclic
two-phase population dynamics including delayed effect of
population density growth on the mortality. Both phases are modelled
as a system of initial boundary values problem for semi-linear
transport equation with delay and initial problem for nonlinear delay
ODE. The obtained system is studied both theoretically and numerically.
Three different regimes of population dynamics for asymptotically
stable states of autonomous systems are obtained in numerical
experiments for the different initial values of population density. The
quasi-periodical travelling wave solutions are studied numerically for
the autonomous system with the different values of time delays and
for the system with oscillating death rate and birth modulus. In both
cases it is observed three types of travelling wave solutions: harmonic
oscillations, pulse sequence and single pulse.