Elementary bifurcations for a simple dynamical system under 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 {\alpha}-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 numerically solving a non local Fokker-Planck equation. This allows numerically investigating phenomenological bifurcation, or   P-bifurcation, for stochastic differential equations with non-Gaussian Levy noises. 
Huiqin Chen, Jinqiao Duan and Chengjian Zhang
math.DS math.AP math.PR