Reducible fractional harmonics generated by the nonautonomous Duffing-Rayleigh equation. Pockets of reducible harmonics and Arnold's tongues

This paper deals with bifurcation structures related to families of fractio nal harmonics (or ultrasubharmonics) solutions generated by the Duffing-Ray leigh equation with a nonsymmetrical periodic external force. It presents s ome results on fractional reducible harmonics and their bifurcations. In pa rticular a new type of contact of fold curves with Neimark's bifurcation cu rves (improperly called ''Hopf bifurcation"), due to such fractional harmon ics, is described. This contact is different from the one related to an Arn old's tongue. The corresponding configuration is called pocket of a reducib le harmnonics.