Frequency locking and devil's staircase for a two-dimensional ferrofluid droplet in an elliptically polarized rotating magnetic field

摘要

Numerical studies reveal that the dynamics of a magnetic fluid droplet under the action of an elliptically polarized rotating magnetic field can be quite complicated, including a transition to a chaotic behavior. On the basis of equations of motion derived by a virial method, the devil's staircase, and its Farey tree structure, is found for the time-averaged angular velocity of the droplet as a function of the angular velocity of the elliptically polarized field. By considering frequency locking (Arnold tongues) with respect to the magnetic Bond number, we establish multiple basins of attraction in different regions of the parameter space. The fractal character of basins of attraction is revealed and phenomena of hysteresis are shown from numerical scanning of the region of control parameters. The existence of period doublings and the transition to chaotic behavior at large field ellipticity parameters is suggested on the basis of phase space plots.