  Frequency locking in forced oscillatory systems typically occurs in
'V'-shaped domains in the plane spanned by the forcing frequency and amplitude,
the so-called Arnol'd tongues. Here, we show that if the medium is spatially
extended and monotonically heterogeneous, e.g., through spatially-dependent
natural frequency, the resonance tongues can also display 'U' and 'W' shapes;
to the latter, we refer as "inverse camel" shape. We study the generic forced
complex Ginzburg-Landau equation for damped oscillations under parametric
forcing and, using linear stability analysis and numerical simulations, uncover
the mechanisms that lead to these distinct shapes. Additionally, we study the
effects of discretization, by exploring frequency locking of oscillators
chains. Since we study a normal-form equation, the results are
model-independent near the onset of oscillations, and, therefore, applicable to
inherently heterogeneous systems in general, such as the cochlea. The results
are also applicable to controlling technological performances in various
contexts, such as arrays of mechanical resonators, catalytic surface reactions,
and nonlinear optics.
