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The resonant behavior of fractional harmonic oscillator with fluctuating mass

Yu Tao Luo Mao-Kang Hua Yun

The resonant behavior of fractional harmonic oscillator with fluctuating mass

Yu Tao, Luo Mao-Kang, Hua Yun
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  • Received Date:  28 May 2013
  • Accepted Date:  23 July 2013
  • Published Online:  05 November 2013

The resonant behavior of fractional harmonic oscillator with fluctuating mass

  • 1. Department of Mathematics, Sichuan University, Chengdu 610064, China;
  • 2. Science and Technology on Electronic Information Control Laboratory, Chengdu 610036, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11171238), and the Science and Technology on Electronic Information Control Laboratory, China (Grant No. 2013035).

Abstract: When moving in viscous medium, the mass of a Brownian particle is fluctuant and its damping force depends on the past velocity history. Therefore, in order to investigate the characteristics of Brownian motion in viscous medium, fractional harmonic oscillator is proposed in this paper for the first time so for as we know. First, the Shapiro-Loginov formula is fractionized to solve fractional stochastic differential equation with exponential correlative stochastic coefficients. Then, by using stochastic averaging method and fractional Shapiro-Loginov formula, the analytical expression of a system’s steady response amplitude is presented and the system’s resonant behavior is discussed accordingly. Finally, the reliability of theoretical results is tested by simulation experiments. All the research shows that: (1) Stochastic resonant behavior can be induced by mass fluctuation noise. (2) Parameter-induced resonance can be induced by memory damping force. (3) Under different parameter conditions, the system’s resonant forms are diverse.

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