  Mathematical models of interacting populations are often constructed as
systems of differential equations, which describe how populations change with
time. Below we study one such model connected to the nonlinear dynamics of a
system of populations in presence of time delay. The consequence of the
presence of the time delay is that the nonlinear dynamics of the studied system
become more rich, e.g., new orbits in the phase space of the system arise which
are dependent on the time-delay parameters. In more detail we introduce a time
delay and generalize the model system of differential equations for the
interaction of three populations based on generalized Volterra equations in
which the growth rates and competition coefficients of populations depend on
the number of members of all populations
\cite{Dimitrova2001a},\cite{Dimitrova2001b} and then numerically solve the
system with and without time delay. We use a modification of the method of
Adams for the numerical solution of the system of model equations with time
delay. By appropriate selection of the parameters and initial conditions we
show the impact of the delay time on the dynamics of the studied population
system.
