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Overdamped fractional Langevin equation and its stochastic resonance

Gao Shi-Long Zhong Su-Chuan Wei Kun Ma Hong

Overdamped fractional Langevin equation and its stochastic resonance

Gao Shi-Long, Zhong Su-Chuan, Wei Kun, Ma Hong
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  • Received Date:  11 August 2011
  • Accepted Date:  28 May 2012
  • Published Online:  20 May 2012

Overdamped fractional Langevin equation and its stochastic resonance

  • 1. College of Mathematics, Sichuan University, Chengdu 610065, China;
  • 2. College of Mathematics and Information Science, Leshan Normal University, Leshan 614000, China
Fund Project:  Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 10731050) and the China Postdoctoral Science Foundation (Grant No. 20100471651, 201104693).

Abstract: By choosing an appropriate damping kernel function of generalized Langevin equation, fractional Langevin equation (FLE) is derived in the case of overdamped condition. With the theory of anomalous diffusion and the memory of fractional derivatives, the physical meaning of FLE is discussed. Moreover, the internal mechanism of stochastic resonance about FLE is obtained. Finally, the numerical simulation shows that in a certain range of the order, stochastic resonance appears in FLE, and it is evident that the SNR gain in fractional Langevin equation is better than that of the integer-order situation.

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