A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits

作者：Wang, Hui; Chen, Xiaoli; Duan, Jinqiao^*

来源：International Journal of Bifurcation and Chaos, 2018, 28(1): 1850017.

DOI：10.1142/S0218127418500177

• Stochastic pitchfork bifurcation
• Levy motion
• most probable equilibrium states
• nonlocal Fokker-Planck equation
• bifurcation diagrams

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 with 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 no 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.

• 出版日期2018-1
• 单位华中科技大学