title: Bifurcation dynamics of the tempered fractional Langevin equation.
abstract: 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.
authors: School of Mathematics, South China University of Technology, Guangzhou 510640, People's Republic of China.
authors: Caibin
authors: C
authors: Zeng
authors: School of Mathematics, South China University of Technology, Guangzhou 510640, People's Republic of China.
authors: Qigui
authors: Q
authors: Yang
authors: MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343, USA.
authors: YangQuan
authors: Y
authors: Chen