Cell-mapping description of coexisting phase-locked soliton states in a long ac-biased Josephson junction

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Abstract
The coexistence of phase-locked soliton states in a long ac-biased Josephson junction is pointed out on the basis of numerical calculations. We use a combined interpolation and cell-mapping technique to calculate periodic orbits along with their stability and basins of attraction. The dominant coexistent phase-locked states consist of the well-known zero-field step (shuttling regime of solitons) and the so-called C-cycle dynamics. In the latter the soliton is bouncing only at one end of the junction, therefore producing no average voltage. The probability of reaching the basins of attraction of these different motions explains the hysteresis and the complicated fine structure in the current-voltage curve obtained from the model equation.