Tangent bifurcation in doubling period process of a resonant circuit's responses

Some qualitative properties and bifurcations of periodic responses in a resonant circuit described by a Duffing's equation with a sinusoidal forcing term are investigated. According to the variation of one parameter related to the input signal we confirm the correlation between the bifurcation curves and the higher harmonics oscillations such a result has been obtained in former studies for a different circuit and in different parameter plane. The most characteristic phenomenon observed in resonant circuit is the occurrence of tangent bifurcation within a doubling period process. We also identify the Pitchfork bifurcation of 2n/spl pi/-periodic solutions for n>1.