A new procedure for exploring chaotic attractors in nonlinear dynamical systems under random excitations  

作　　者：Chun-Biao Gan Hua Lei 

机构地区：[1]Department of Mechanical Engineering,Zhejiang University,310027 Hangzhou, China [2]Institute of Applied Mechanics, SAA,Zhejiang University,310027 Hangzhou, China

出　　处：《Acta Mechanica Sinica》2011年第4期593-601,共9页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (10672140,11072213)

摘　　要：Due to uncertain push-pull action across boundaries between different attractive domains by random excitations, attractors of a dynamical system will drift in the phase space, which readily leads to colliding and mixing with each other, so it is very difficult to identify irregular signals evolving from arbitrary initial states. Here, periodic attractors from the simple cell mapping method are further iterated by a specific Poincare map in order to observe more elaborate structures and drifts as well as possible dynamical bifurcations. The panorama of a chaotic attractor can also be displayed to a great extent by this newly developed procedure. From the positions and the variations of attractors in the phase space, the action mechanism of bounded noise excitation is studied in detail. Several numerical examples are employed to illustrate the present procedure. It is seen that the dynamical identification and the bifurcation analysis can be effectively performed by this procedure.Due to uncertain push-pull action across boundaries between different attractive domains by random excitations, attractors of a dynamical system will drift in the phase space, which readily leads to colliding and mixing with each other, so it is very difficult to identify irregular signals evolving from arbitrary initial states. Here, periodic attractors from the simple cell mapping method are further iterated by a specific Poincare map in order to observe more elaborate structures and drifts as well as possible dynamical bifurcations. The panorama of a chaotic attractor can also be displayed to a great extent by this newly developed procedure. From the positions and the variations of attractors in the phase space, the action mechanism of bounded noise excitation is studied in detail. Several numerical examples are employed to illustrate the present procedure. It is seen that the dynamical identification and the bifurcation analysis can be effectively performed by this procedure.

关 键 词：Dynamical system Bounded noise excitationPoincare map Chaotic attractor. Bifurcation 

分 类 号：O415.5[理学—理论物理] O324[理学—物理]