  A scenario has recently been reported in which in order to stabilize complete
synchronization of an oscillator network---a symmetric state---the symmetry of
the system itself has to be broken by making the oscillators nonidentical. But
how often does such behavior---which we term asymmetry-induced synchronization
(AISync)---occur in oscillator networks? Here we present the first general
scheme for constructing AISync systems and demonstrate that this behavior is
the norm rather than the exception in a wide class of physical systems that can
be seen as multilayer networks. Since a symmetric network in complete synchrony
is the basic building block of cluster synchronization in more general
networks, AISync should be common also in facilitating cluster synchronization
by breaking the symmetry of the cluster subnetworks.
