  The paper revisits recently revealed regimes of the "nonconventional
synchronization" in systems of coupled bi-stable Van der Pol oscillators. These
regimes are characterized by periodic (or quasiperiodic) almost complete energy
exchanges between the coupled oscillators. In the paper it is demonstrated that
such responses correspond to synchronization of the modulation amplitudes
between symmetric and antisymmetric modes of the system, with persistent phase
drift. This observation substantially simplifies the treatment, reduces the
dynamics to simple phase cylinder and allows to reveal a rich set of global and
local bifurcations of limit cycles and tori in the system. Among other
findings, one encounters an unexpected regime of nonstationary asymmetric
synchronization.
