Relaxation oscillations in slow-fast IS-LM economic models

We consider the dynamics of the IS-LM economic model, which is a fundamental macroeconomic model describing the relationship between interest rates and assets market. There is generally a long time lag between changes in the interest rate and the consequential effects on the economy. Therefore, most central banks change the interest rates slowly, which yields a slow-fast IS-LM model. Using geometric singular perturbation theory, we establish the sufficient and necessary conditions on the existence of relaxation oscillations for the slow-fast IS-LM model. We also apply our abstract genericity results to study some concrete particular slow-fast IS-LM models. Numerical simulations are presented to validate the theoretical results.