  We consider the model of economic growth with time delayed investment
function. Assuming the investment is time distributed we can use the linear
chain trick technique to transform delay differential equation system to
equivalent system of ordinary differential system (ODE). The time delay
parameter is a mean time delay of gamma distribution. We reduce the system with
distribution delay to both three and four-dimensional ODEs. We study the Hopf
bifurcation in these systems with respect to two parameters: the time delay
parameter and the rate of growth parameter. We derive the results from the
analytical as well as numerical investigations. From the former we obtain the
sufficient criteria on the existence and stability of a limit cycle solution
through the Hopf bifurcation. In numerical studies with the Dana and Malgrange
investment function we found two Hopf bifurcations with respect to the rate
growth parameter and detect the existence of stable long-period cycles in the
economy. We find that depending on the time delay and adjustment speed
parameters the range of admissible values of the rate of growth parameter
breaks down into three intervals. First we have stable focus, then the limit
cycle and again the stable solution with two Hopf bifurcations. Such behaviour
appears for some middle interval of admissible range of values of the rate of
growth parameter.
