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

TL;DR

This paper investigates bifurcations in a simple stochastic dynamical system influenced by non-Gaussian Levy noises, using numerical solutions of a non-local Fokker-Planck equation to analyze changes in stationary probability densities.

Contribution

It introduces a computational approach to study P-bifurcations in stochastic systems under Levy noise by solving a non-local Fokker-Planck equation.

Findings

Identification of bifurcation phenomena via stationary density changes

Numerical method for non-Gaussian noise-driven systems

Insights into stochastic bifurcation behavior under Levy noise

Abstract

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.