Non-conventional phase attractors and repellers in weakly coupled autogenerators with hard excitation

EPL. 2017. Vol. 120. No. 30007. P. 1–6.

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

In our earlier studies, we found the effect of non-conventional synchronization, which
is a specific type of nonlinear stable beating in the system of two weakly coupled autogenerators
with hard excitation given by generalized van der Pol-Duffing characteristics. The corresponding
synchronized dynamics are due to a new type of attractor in a reduced phase space of the system.
In the present work, we show that, as the strength of nonlinear stiffness and dissipation are
changing, the phase portrait undergoes a complicated evolution leading to a quite unexpected
appearance of difficult to detect “repellers” separating a stable limit cycle and equilibrium points
in the phase plane. In terms of the original coordinates, the limit cycle associates with nonlinear
beatings while the stationary points correspond to the stationary synchronous dynamics similar
to the so-called nonlinear local modes.

Keywords: Frequency and Time Synchronization, coupled oscillators