  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.
