Acta mathematica scientia, Series B >
ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LÉVY NOISES
Received date: 2010-12-10
Revised date: 2011-04-15
Online published: 2012-07-20
Supported by
This work was partly 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).
Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical sys-tems when a parameter varies.
A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian α-stable L´evy motions, by examining the changes in station-ary 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 L´evy noises.
CHEN Hui-Qin , DUAN Jin-Qiao , ZHANG Cheng-Jian . ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LÉVY NOISES[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1391 -1398 . DOI: 10.1016/S0252-9602(12)60107-6
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