Nonconventional synchronization and energy localization in weakly coupled autogenerators

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2016. Vol. 94. No. 032223. P. 032223-1–032223-10.

Kovaleva Margarita, Pilipchuk V., Manevitch L. I.

The present work follows our previous study dealing with a new type of synchronization in a system of two
weakly coupled generalized van der Pol–Duffing autogenerators. The essence of the effect revealed is that the
synchronized oscillations are not stationary but accompanied by the most intensive energy exchange between
the oscillators. The phase shift between the generators remains constant most of the time, except for vanishingly
small transitional intervals. The current analysis deals with a generalized model in order to clarify the frequency
detuning effect. We found that varying the frequency detuning, nonlinearity, and dissipation parameters can lead
to structural changes in phase diagrams of the energy exchange dynamics, with important transitions from the
intensive energy exchange to its localization on one of the two oscillators. The main conclusion is that stationary
and nonstationary synchronizations associate with nonlinear normal and local modes, respectively. The analysis
uses phase plane diagrams, including the concept of limiting phase trajectories, whose role in nonstationary
synchronization appears to be similar to the role of nonlinear normal modes in conventional stationary states.

Keywords: синхронизация, energy transfer, synchronization of oscillators, energy localization, coupled oscillstors, связанные осцилляторы, локализация энергии, энергообмен