Hopf bifurcation in the IS-LM business cycle model with time delay

The distinction between investment decisions and implementation leads us to formulate a new IS-LM business cycle model. It is shown that the dynamics depends crucially on the time delay parameter - the gestation time period of investment. The Hopf bifurcation theorem is used to predict the occurrence of a limit cycle bifurcation for the time delay parameter. Our analysis shows that the limit cycle behavior is independent of the assumption of nonlinearity of the investment function. An example is given to verify the theoretical results.