REDUCIBLE FRACTIONAL HARMONICS GENERATED BY THE NONAUTONOMOUS DUFFING–RAYLEIGH EQUATION: POCKETS OF REDUCIBLE HARMONICS AND ARNOLD'S TONGUES

Abstract

This paper deals with bifurcation structures related to families of fractional harmonics (or ultra-subharmonics) solutions generated by the Duffing–Rayleigh equation with a nonsymmetrical periodic external force. It presents some results on fractional reducible harmonics and their bifurcations. In particular a new type of contact of fold curves with Neimark's bifurcation curves (improperly called "Hopf bifurcation"), due to such fractional harmonics, is described. This contact is different from the one related to an Arnold's tongue. The corresponding configuration is called pocket of a reducible harmnonics.