Stability of Limit Cycle in a Delayed IS-LM Business Cycle model

We consider the existence of a local Hopf bifurcation in a nonlinear mixed IS-LM business cycle model. We establish an explicit algorithm for determining the direction of the Hopf bifurcation and the stability or instability of the bifurcating branch of periodic solutions. In the end, we give some numerical simulations which show the existence and the nature of the periodic solutions.