Abstract
AbstractThe bifurcation structure of fractional harmonic entrainments in the forced Rayleigh equation is analyzed in connection with the symmetry of the system. Due to the symmetry of the system, there are two types of fractional harmonic entrainment regions. One is the case in which an attractor symmetric in shape with respect to the origin is generated in the state space. Another is the case in which two attractors in an asymmetric shape appear in locations symmetric with respect to the origin. When the shapes of these bifurcation structures are studied on the parameter surface, it is found that the fractional harmonic entrainment regions of the two cases have different structures near the Neimark–Sacker bifurcation curve of the fundamental harmonic periodic solutions. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(3): 30–40, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10126
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