Chaos in a Model of Credit Cycles with Good and Bad Projects

We consider a credit cycle model introduced by Matsuyama, which is defined by a one-dimensional piecewise smooth map with upward, downward and flat branches. We offer a detailed analysis of this model for the case where asymp- totic dynamics does not involve the flat branch, under the additional assumption that the production function is Cobb-Douglas. In particular, using skew tent map (which is a one-dimensional map defined by two linear functions) as a border collision normal form we obtain conditions of abrupt transition from an attracting fixed point to an attracting cycle or a chaotic attractor (cyclic chaotic intervals). These conditions allow us to describe the overall bifurcation structure of the parameter space of the map in a neighborhood of the boundary related to the border collision bifurcation of the fixed point. Such a structure confirms, in particular, that chaotic attractors of the considered map are robust, that is, they are persistent under parameter perturbations.