Elementary bifurcations for a simple dynamical system under non-Gaussian Levy noises

Details Elementary bifurcations for a simple dynamical system under non-Gaussian Levy noises Elementary bifurcations for a simple dynamical system under non-Gaussian Levy noises

2012-01-29

arxiv.org/abs/1201.6017v1

Mathematics

Dynamical Systems

priprint

Scientific paper

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.

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