Dissipative Effect of Stochastic Excitation on Dynamic Behavior of Softening Duffing Oscillator
Guo Yunsong,Gan Chunbiao,Ye Min
(Department of Mechanics, Zhejiang University, Hangzhou, 310027)

Abstract: The effects of stochastic excitation on the period-doubling bifurcation and chaotic motions of the softening Duffing oscillator, are discussed in detail. With Monte-Carlo method, various eroded safe basins of the system are obse rved, then the reasonable initial value is picked up for the subsequent dynamic analysis. The numerical results from the phase portraits, the period-doubling bifurcation and the Poincare sections show that external stochastic excitation always masks the regular motions of a deterministic system and plays a dissipa tive role to the motions of the system, which causes the chaotic motions of the system to arise easily, though the period-doubling bifurcation is delayed.
Keywords: bounded stochastic excitation, safe basin, period-doubling bifurcation, chaos, Monte-carlo simulation.