Bifurcations in parametrically forced magnetic pendulum

Bifurcations in parametrically forced magnetic pendulum

An experimental study of bifurcations associated with the stability of stationary points(SP's) in a parametrically forced magnetic pendulum, and a comparison of its results with numerical results, are persented. The critical values for which the SP's lose or gain their stability are experimentally measured by varying the two parameters Ω(the normalized natural frequency) and A (the normalized driving amplitude). It is observed that, when the amplitude A exceeds a critical value, the normal SP with θ=0(θ is the angle between the permanent magnet and the magnetic field) becomes unstable either by a period-doubling bifurcation or by a symmetry breaking pitchfork bifurcation, depending on the values of Ω. However, in contrast with the normal SP the inverted SP, with θ=π is observed to become stable as A is increased above a critical value by a pitchfork bifurcation, but it also destabilizes for a higher critical value of A by a period-doubling bifurcation. All of these experimental results agree well with numerical results obtained using Floquet theory. [S1063-651X(97) 06212-0]