Growing through chaotic intervals

We consider a growth model proposed by Matsuyama [K. Matsuyama, Growing through cycles, Econometrica 67 (2) (1999) 335–347] in which two sources of economic growth are present: the mechanism of capital accumulation (Solow regime) and the process of technical change and innovations (Romer regime). We will shown that no stable cycle can exist, except for a fixed point and a cycle of period two. The Necessary and Sufficient conditions for regular or chaotic regimes are formulated. The bifurcation structure of the two-dimensional parameter plane is completely explained. It is shown how the border-collision bifurcation leads from the stable fixed point to pure chaotic regime (which consists either in 4-cyclical chaotic intervals, 2-cyclical chaotic intervals or in one chaotic interval).