title: Comparison of winding-number sequences for symmetric and asymmetric oscillatory systems.
abstract: The bifurcation sets of symmetric and asymmetric periodically driven oscillators are investigated and classified by means of winding numbers. It is shown that periodic windows within chaotic regions are forming winding-number sequences on different levels. These sequences can be described by a simple formula that makes it possible to predict winding numbers at bifurcation points. Symmetric and asymmetric systems follow similar rules for the development of winding numbers within different sequences and these sequences can be combined into a single general rule. The role of the two distinct period-doubling cascades is investigated in the light of the winding-number sequences discovered. Examples are taken from the double-well Duffing oscillator, a special two-parameter Duffing oscillator, and a bubble oscillator.
authors.affiliation: 17712 Crystal Spring Terrace, Ashton, Maryland 20861, USA.
authors.forename: Volker
authors.initials: V
authors.lastname: Englisch
authors.affiliation: Biomedical Physics Group, Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen, Germany.
authors.forename: Ulrich
authors.initials: U
authors.lastname: Parlitz
authors.affiliation: Drittes Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany.
authors.forename: Werner
authors.initials: W
authors.lastname: Lauterborn
mesh_terms: D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D010507:Periodicity