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Suppression of phase-locking chaos in long Josephson junctions by biharmonic microwave fields.

We consider the problem of phase locking of fluxon oscillations in long Josephson junctions irradiated by an external microwave field consisting of two harmonic signals, one at frequency {omega} and the other at frequency {omega}/2 added together (biharmonic driver). The analysis is performed in terms of a two-dimensional map constructed in terms of the fluxon time of flight and fluxon's energy inside the junction. As a result we find that the second driver enhances the stability of the phase-locking state and can be used to suppress the phase-locking chaos in the middle of the step induced by the first driver.