Bifurcation Theory in Dynamical Economics

Abstract

This chapter deals with a subject that has become a major focus of research in dynamical economics during the last decade, namely bifurcation theory. Central to this topic is the question whether the qualitative properties of a dynamical system change when one or more of the exogenous parameters are changing. In contrast to the physical sciences, it is usually impossible to assign a definitive, once-and-for-all valid number to most parameters occurring in dynamical systems in economics. Parameters are introduced into an economic model in order to reflect the influence of exogenous forces which are either beyond the scope of pure economic explanation or which are intentionally considered as being exogenously given from the point of view of partial theorizing. It is desirable to determine whether the qualitative behavior of a dynamical system persists under variations in the parameter space. Thus, the results of bifurcation theory are especially important to dynamic modelling in economics.