ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LVY NOISES

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 α-stable Lévy 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 Lévy noises.