On the behavior of characteristic multipliers through a period-doubling sequence

Initial work along these lines by the present authors has focused attention on how these ideas can be used to infer and predict the loss of stability of an n = 1 solution. Here, the algorithm is applied through a series of period-doubling bifurcations, but certain practical limitations operate [2]. These include problems associated with the length of transient decay and magnitude of the perturbation used. This brief note shows that it is possible to track the stability of increasingly high order subharmonic oscillations through a period-doubling sequence using a careful numerical approach. It is also shown that the passage through this sequence results in the scaling of successive CM radii if the forcing amplitude is used as the control parameter.

Duke Scholars

Author Lawrence N. Virgin Thomas Lord Department of Mechanical Engineering and Materia ...