  We consider entrainment by periodic force of limit cycles which are close to
the homoclinic bifurcation. Taking as a physical example the nanoscale
spin-torque oscillator in the LC circuit, we develop the general description of
the situation in which the frequency of the stable periodic orbit in the
autonomous system is highly sensitive to minor variations of the parameter, and
derive explicit expressions for the strongly deformed borders of the resonance
regions (Arnold tongues) in the parameter space of the problem. It turns out
that proximity to homoclinic bifurcations hinders synchronization of
spin-torque oscillators.

Chaotic Dynamics