Nonlinear dynamics of a damped magnetic oscillator

Nonlinear dynamics of a damped magnetic oscillator

We consider a damped magnetic oscillator (MO). consisting of a permanent magnet in a periodically oscillating magnetic field. A detailed investigation of the dynamics of this dissipative magnetic system is made by varying the field amplitude A. As A is increased. the damped MO, albeit simple looking, exhibits rich dynamical behaviours such as symmetry-breaking pitchfork bifurcations, period-doubling transitions to chaos, symmetry-restoring attractor-merging crises, and saddle-node bifurcations giving rise to new periodic attractors. Besides these familiar behaviours, a cascade of 'resurrections' (Le.. an infinite sequence of alternating restabilizations and destabilizations) of the stationary points also occurs. It is found that the stationary points restabilize (destabilize) through alternating subcritical (supercritical) period-doubling and pitchfork bifurcations. We also discuss the critical behaviours in the period-doubling cascades.