A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits
A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits
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最可能相图中的随机干草叉分叉
DOI：
10.1142/s0218127418500177
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发表时间：
2018
影响因子：
2.2
通讯作者：
Duan Jinqiao
中科院分区：
文献类型：
--
作者：
Wang Hui;Chen Xiaoli;Duan Jinqiao
研究了一类乘性稳定Levy噪声（一类重要的非高斯噪声）作用下系统的随机分岔，通过考察系统平衡态在其最可几相图中的定性变化.我们发现了与确定性分岔不同的一些特殊分岔现象：（1）当Levy噪声中的非高斯参数变化时，有一个、两个或没有后向叉型分岔：（2）当矢量场中的一个参数变化时，有两个或三个前向叉型分岔;（iii）非高斯Levy噪声显然导致从根本上更复杂的分叉场景，因为在高斯噪声的特殊情况下，只有一个干草叉分叉，这让人想起确定性情况。
We study stochastic bifurcation for a system under multiplicative stable Levy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states in its most probable phase portraits. We have found some peculiar bifurcation phenomena in contrast to the deterministic counterpart: (i) When the non-Gaussianity parameter in Levy noise varies, there is either one, two or none backward pitchfork type bifurcations; (ii) When a parameter in the vector field varies, there are two or three forward pitchfork bifurcations; (iii) The non-Gaussian Levy noise clearly leads to fundamentally more complex bifurcation scenarios, since in the special case of Gaussian noise, there is only one pitchfork bifurcation which is reminiscent of the deterministic situation.