Eur. Phys. J. Plus (2017) 132: 2
https://doi.org/10.1140/epjp/i2017-11273-7

Regular Article

Random-order fractional bistable system and its stochastic resonance

¹ College of Mathematics and Information Science, Leshan Normal University, 614000, Leshan, China
² Applied Mathematics Research Center, Leshan Normal University, 614000, Leshan, China
³ Editorial Department, Journal of Leshan Normal University, 614000, Leshan, China

^* e-mail: lunan1027@126.com

Received: 24 September 2016
Accepted: 28 November 2016
Published online: 12 January 2017

Abstract

In this paper, the diffusion motion of Brownian particles in a viscous liquid suffering from stochastic fluctuations of the external environment is modeled as a random-order fractional bistable equation, and as a typical nonlinear dynamic behavior, the stochastic resonance phenomena in this system are investigated. At first, the derivation process of the random-order fractional bistable system is given. In particular, the random-power-law memory is deeply discussed to obtain the physical interpretation of the random-order fractional derivative. Secondly, the stochastic resonance evoked by random-order and external periodic force is mainly studied by numerical simulation. In particular, the frequency shifting phenomena of the periodical output are observed in SR induced by the excitation of the random order. Finally, the stochastic resonance of the system under the double stochastic excitations of the random order and the internal color noise is also investigated.