A new criterion of period-doubling bifurcation in maps and its application to an inertial impact shaker

A new critical criterion of period-doubling bifurcations is proposed for high dimensional maps. Without the dependence on eigenvalues as in the classical bifurcation criterion, this criterion is composed of a series of algebraic conditions under which period-doubling bifurcation occurs. The proposed criterion is applied to the analysis of period-doubling bifurcation in a two-degree-of-freedom inertial shaker model. It can be seen in this example that the proposed criterion is preferable to the classical bifurcation criterion in high dimensional maps.