“Period three to period two” bifurcation for piecewise linear models

In Hommes, Nusse, and Simonovits (1990) the dynamics of a simple economic model was studied. Although this piecewise linear model is quite simple, its dynamics shows different kinds of behavior such as periodic, quasiperiodic, and chaotic behavior. In particular, a new kind of bifurcation, namely a period three to period two bifurcation, was observed numerically. This paper deals with this new bifurcation phenomenon and we show that the “period three to period two” bifurcation occurs and is a structurally stable phenomenon in a class of two-dimensional continuous, piecewise linear systems. In particular, the “period three to period two” bifurcation is a structurally stable phenomenon in economic models with Hicksian nonlinearities