Bifurcations in economic growth model with distributed time delay transformed to ODE
Abstract
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 fourdimensional 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 longperiod 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.05016
 Bibcode:
 2020arXiv200205016G
 Keywords:

 Economics  Theoretical Economics;
 Economics  General Economics;
 Mathematics  Dynamical Systems
 EPrint:
 20 pages, 11 figures