Resonance phenomena in nonlinear parametrically driven systems

A new physical effect describing the nonlinear behavior of magnetically (electrically) anisotropic objects in an external field is described. These objects (large particles or cluster of particles in solutions) acquire an induced moment in a direction different than that of the field. Only objects at special sizes confined from above and below are able to rotate (vibrate) and to transfer energy from an external field to the media. The numerical solution of the appropriate parametrically-driven oscillator equation manifests a whole variety of non-linear dynamic behaviour: periodic solutions with Feigenbaum doubled frequencies, strange attractors indicating chaos, etc. The experimental verification of the theory can be performed by susceptibility or birefringence measurements. The suggested effect exists also for particles with permanent magnetic (electric) moments.