ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LVY NOISES  

作　　者：陈慧琴 段金桥 张诚坚 

机构地区：[1]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China [2]School of Mathematics and Computer Science,Jianghan University,Wuhan 430056,China [3]Department of Applied Mathematics,Illinois Institute of Technology,Chicago,IL 60616,USA

出　　处：《Acta Mathematica Scientia》2012年第4期1391-1398,共8页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(10971225, 11171125, 91130003 and 11028102);the NSFH (2011CDB289);HPDEP (20114503 and 2011B400);the Cheung Kong Scholars Program and the Fundamental Research Funds for the Central Universities, HUST(2010ZD037)

摘　　要：Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian a-stable Levy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Levy noises.Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian a-stable Levy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Levy noises.

关 键 词：stochastic dynamical systems non-Gaussian Levy motion Levy jump mea-sure stochastic bifurcation impact of non-Gaussian noises 

分 类 号：O211.63[理学—概率论与数理统计] O19[理学—数学]