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Advances in Mathematical Physics
Volume 2016, Article ID 5164575, 12 pages
Research Article

The Stochastic Resonance Behaviors of a Generalized Harmonic Oscillator Subject to Multiplicative and Periodically Modulated Noises

1College of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China
2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
3College of Mathematics, Sichuan University, Chengdu 610065, China

Received 21 September 2016; Revised 9 November 2016; Accepted 20 November 2016

Academic Editor: Maria L. Gandarias

Copyright © 2016 Suchuan Zhong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The stochastic resonance (SR) characteristics of a generalized Langevin linear system driven by a multiplicative noise and a periodically modulated noise are studied (the two noises are correlated). In this paper, we consider a generalized Langevin equation (GLE) driven by an internal noise with long-memory and long-range dependence, such as fractional Gaussian noise (fGn) and Mittag-Leffler noise (M-Ln). Such a model is appropriate to characterize the chemical and biological solutions as well as to some nanotechnological devices. An exact analytic expression of the output amplitude is obtained. Based on it, some characteristic features of stochastic resonance phenomenon are revealed. On the other hand, by the use of the exact expression, we obtain the phase diagram for the resonant behaviors of the output amplitude versus noise intensity under different values of system parameters. These useful results presented in this paper can give the theoretical basis for practical use and control of the SR phenomenon of this mathematical model in future works.