Abstract
A numerical and analytical study is presented here which suggests that jump phenomena and chaotic motion are possible from periodic excitation of nonlinear system of a single degree of freedom which includes the Duffing equation as a special case. Approximate analytical technilues (averaging method and Bogoliuboff-Mitropolsky method) are applied to obtain some of the resonance curves, and the chaotic motions are investigated by using the Poincare map, Li-Yorke's theorem, the Liapunov exponent, the invariant probability distribution and Mel'nikov's method.
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