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Fluctuations in a Delayed IS-LM Business Cycle Model

Abdelilah Kaddar, Boujema Talibi Alaoui


We formulate a delayed IS-LM business cycle model by introducing a time delay into gross product, capital stock and interest rate. The dynamics are studied in terms of local stability and of the description of the Hopf bifurcation, that is proven to exists as the delay (taken as a parameter of bifurcation) cross some critical value. Additionally an explicit algorithm is established to determine the direction of the Hopf bifurcation and the stability or instability of the bifurcating branch of periodic solutions. In the end some numerical simulations are given to show the existence and the nature of the periodic solutions.

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