In the present paper we investigate two-parametric family of nonautonomous ordinary differential equations on the two-torus that model the Josephson effect from superconductivity. We study its rotation number as a function of parameters and its Arnold tongues (also called phase locking domains): the level sets of the rotation number that have non-empty interior. The Arnold tongues of the equation under consideration have many non-typical properties: the phase locking happens only for integer values of the rotation number [5, 11]; the boundaries of the tongues are given by analytic curves [4, 7], the tongues have zero * Laboratoire J.-V.Poncelet (UMI 2615 du
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