Periodic Dzhanibekov-like transitions of the double pendulum

The double pendulum is a well-known nonlinear dynamic system. Many previous studies considered one or more of its three categories of response: periodic (a.k.a. normal), regular (a.k.a. quasi-periodic), and chaotic. In this study, we show a new fourth category of response that we term Dzhanibekov-like transitions. It begins with a nearly periodic response, then in a fast transition, it diverges and converges to a second nearly periodic response. These sequential transitions between the two nearly periodic responses are repeated at regular time intervals. We demonstrate symmetric and asymmetric Dzhanibekov-like transitions. Five different metrics of the dynamic response are used to distinguish between a common regular response and Dzhanibekov-like transitions.