Bifurcation dynamics of the tempered fractional Langevin equation
- School of Mathematics, South China University of Technology, Guangzhou 510640 (China)
- MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
- OSTI ID:
- 22596560
- Journal Information:
- Chaos (Woodbury, N. Y.), Vol. 26, Issue 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 1054-1500
- Country of Publication:
- United States
- Language:
- English
Similar Records
Fractional noise destroys or induces a stochastic bifurcation
Quantum theory of open systems based on stochastic differential equations of generalized Langevin (non-Wiener) type