Stability and Hopf bifurcation analysis of a distributed time delay energy model for sustainable economic growth

Abstract

This paper examines the consequences of including distributed delays in an energy model. The stability behaviour of the resulting equilibrium for our dynamic system is analysed, including models with Dirac, weak and strong kernels. Applying the Hopf bifurcation theorem we determine conditions under which limit cycle motion is born in such models. The results indicate that distributed delays have an ambivalent impact on the dynamical behaviour of systems, either stabilizing or destabilizing them.