A kind of noise-induced transition to noisy chaos in stochastically perturbed dynamical system  

作　　者：Chun-Biao Gan Shi-Xi Yang Hua Lei 

机构地区：[1]Department of Mechanical Engineering,Zhejiang University [2]Department of Engineering Mechanics,Zhejiang University

出　　处：《Acta Mechanica Sinica》2012年第5期1416-1423,共8页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (11172260 and 11072213);the Fundamental Research Fund for the Central University of China (2011QNA4001)

摘　　要：We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar6 map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar6＇s cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincare＇s global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar6 map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar6＇s cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincare＇s global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.

关 键 词：Stochastic excitation - Dynamical system - Specific Poincare map Noise-induced transition to chaos 

分 类 号：O415.5[理学—理论物理] O19[理学—物理]