  Large ensembles of heterogeneous oscillators often exhibit collective
synchronization as a result of mutual interactions. If the oscillators have
distributed natural frequencies and common shear (or nonisochronicity), the
transition from incoherence to collective synchronization is known to occur at
large enough values of the coupling strength. However, here we demonstrate that
shear diversity cannot be counterbalanced by diffusive coupling leading to
synchronization. We present the first analytical results for the Kuramoto model
with distributed shear, and show that the onset of collective synchronization
is impossible if the width of the shear distribution exceeds a precise
threshold.
