Applications of stochastic sensitivity function method in non-autonomous nonlinear systems
GUO Kong-ming 1 JIANG Jun 2
1 School of Electronic and Mechanical Engineering, Xidian University, Xi’an 710071, China;
2. State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049,China
Abstract：Distribution characters of periodic attractors in non-autonomous differential dynamical systems disturbed by weak Gaussian white noise were studied. Based on stroboscopic mapping, differential dynamical systems were discretized into maps. Through solving stochastic sensitivity functions of periodic attractors in maps, confidence ellipses were constructed to describe the distributions of the random attractors. In this way, boundary value problems of matrix differential equations were avoided, and only matrix algebra equations need to be solved. Distributions of stochastic periodic attractors in Duffing equation were studied. The results show that confidence ellipses achieved good agreement with the Monte-Carlo simulation. Finally, noise-induced chaos in Duffing equation was researched qualitatively, it was proven that stochastic sensitivity function can reveal the mechanism of this phenomenon.
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