Stability and Hopf Bifurcation of a Fractional Economic Model with Time Delay

Abstract

In this paper, a fractional order economic model with time delay is proposed and its related dynamics is studied. We mainly study the equilibrium stability of the system and the existence of Hopf bifurcation. By taking the time delay as the bifurcation parameter and analysing the characteristic equation, we find that when the time delay exceeds a certain range, the system will lose stability. The results show the stability at the positive equilibrium point of the system depends on the critical value of time delay. Finally, the correctness of the theories obtained are verified by numerical simulations.