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

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.