Period doubling bifurcation and chaos observed in regions of higher-harmonic entrainment in the forced Rayleigh oscillator

In this article, bifurcation phenomena from the fundamental to the sixth hi gher-harmonic entrainment of a forced Rayleigh oscillator are studied. Of t he fundamental to the sixth higher-harmonic entrainment regions, the saddle node bifurcation draws a closed loop, and no complex; bifurcation structur es are seen on the odd higher-harmonic entrainment region. In the even high er-harmonic entrainment region, a symmetry-breaking bifurcation is generate d when the saddle node bifurcation approaches the Neimark Sacker bifurcatio n. Subsequently, period-doubling bifurcation is generated so that chaos is also generated. (C) 2000 Scripta Technica.