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Stability criteria and fluctuations for a business cycle model

Mohamed El Fatini, Abdelilah Kaddar, Aziz Laaribi


The IS-LM model of business cycles, was treated as a good attempt to explain the fluctuations in economic activities. It concludes that the nonlinearity in the investment and saving processes has absolutely an effect on the economic fluctuations. But the time delay in IS-LM model with linear investment function and linear saving function can destabilise the economic system giving rise to economic oscillations. According to Hopf bifurcation theory, we investigate an IS-LM model with time delay in the investment function and capital stock depreciation. We show that the resulting model gives rise to the bifurcating branch of periodic solutions. We also determine the stability of the obtained bifurcating branch.


IS-LM business cycle, delayed differential equations, Hopf bifurcation, periodic solutions.

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