The maximal Lyapunov exponent of a co-dimension two-bifurcation system excited by a bounded noise  

作　　者：Sheng-Hong Li Xian-Bin Liu 

机构地区：[1]State Key Lab of Mechanics and Control for Mechanical Structures,College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,210014 Nanjing,China [2]School of Mathematics and Physics,Jiangsu University of Science and Technology,212003 Zhenjiang,China

出　　处：《Acta Mechanica Sinica》2012年第2期511-519,共9页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (11072107,91016022);the Specialized Research Fund for the Doctoral Program of Higher Education of China(20093218110003)

摘　　要：In the present paper, the maximal Lyapunov ex- ponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise. By using a perturbation method, the expressions of the invari- ant measure of a one-dimensional phase diffusion process are obtained for three cases, in which different forms of the matrix B, that is included in the noise excitation term, are assumed and then, as a result, all the three kinds of singular boundaries for one-dimensional phase diffusion process are analyzed. Via Monte-Carlo simulation, we find that the an- alytical expressions of the invariant measures meet well the numerical ones. And furthermore, the P-bifurcation behav- iors are investigated for the one-dimensional phase diffusion process. Finally, for the three cases of singular botmdaries for one-dimensional phase diffusion process, analytical ex- pressions of the maximal Lyapunov exponent are presented for the stochastic bifurcation system.In the present paper, the maximal Lyapunov ex- ponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise. By using a perturbation method, the expressions of the invari- ant measure of a one-dimensional phase diffusion process are obtained for three cases, in which different forms of the matrix B, that is included in the noise excitation term, are assumed and then, as a result, all the three kinds of singular boundaries for one-dimensional phase diffusion process are analyzed. Via Monte-Carlo simulation, we find that the an- alytical expressions of the invariant measures meet well the numerical ones. And furthermore, the P-bifurcation behav- iors are investigated for the one-dimensional phase diffusion process. Finally, for the three cases of singular botmdaries for one-dimensional phase diffusion process, analytical ex- pressions of the maximal Lyapunov exponent are presented for the stochastic bifurcation system.

关 键 词：Maximal Lyapunov exponent Perturbationmethod. Bounded noise. Diffusion process 

分 类 号：O415.5[理学—理论物理] TP13[理学—物理]