Abstract
The paper presents a numerical analysis of the characteristic of regular motion besides the chaotic behavior in an asymmetrical Duffing's oscillator. By making use of a computer simulation and approximate analytical method, it is shown that compared with the standard Duffing's system, the resonance curves become quite complex, and then there exist the isolated subharmonic vibrations of the 1/2 and 1/3 order, jump phenomena and chaotic phenomena in the frequency region of ultraharmonic oscillations. In addition, the system exhibits chaotic phenomena in the frequency zone of 1/2 subharmonic resonance. Chaotic behavior is discussed with regard to the Poincare mapping and Lyapunov exponent. Furthermore, the basin of attraction of chaotic and regular motions is determined by means of cell mapping.
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