We consider entrainment by periodic force of limit cycles which are close tothe homoclinic bifurcation. Taking as a physical example the nanoscalespin-torque oscillator in the LC circuit, we develop the general description ofthe situation in which the frequency of the stable periodic orbit in theautonomous system is highly sensitive to minor variations of the parameter, andderive explicit expressions for the strongly deformed borders of the resonanceregions (Arnold tongues) in the parameter space of the problem. It turns outthat proximity to homoclinic bifurcations hinders synchronization ofspin-torque oscillators.
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