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Dynamic analysis and numerical simulation of a discrete model of a bistable system†

Published online by Cambridge University Press:  04 September 2014

DINGXIN YANG  and
ZHENG HU
DINGXIN YANG
Affiliation:
College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha, China Email: [email protected]; [email protected]
ZHENG HU
Affiliation:
College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha, China Email: [email protected]; [email protected]
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Abstract

Numerical simulation is the generally used method for studying stochastic resonance (SR), which is a kind of non-linear phenomenon that usually occurs in non-linear bistable systems. It has been found that the input signal needs to be over-sampled during the numerical simulation of SR. In this paper we provide an explanation of this phenomenon based on a stability analysis of the bistable system. We begin by studying the stability of a discrete model of a bistable system in numerical simulations. We then give a theoretical derivation of the stability conditions for the simulation model with different parameters, and carry out numerical experiments to show that the results coincide with the predictions of the theory. We explain why the input signal needs to be over-sampled in the simulation and provides guidelines for the choice of system parameters for the bistable system and the sampling time step in the numerical simulation of SR. Finally, we present the results of simulations showing an example of SR occurring in a bistable system and an example of weak periodic signal detection when it is processed by a bistable system.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Special Issue 5: Mathematical Method in Intelligent Computing and Automation , October 2014 , e240522
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

†

This work was supported by NSFC 50905184.

References

Asdi, A. S. and Tewfik, A. H. (1995) Detection of weak signals using adaptive stochastic resonance. Acoustics, Speech, and Signal Processing 10 (2)1332–1335.Google Scholar
Benzi, R., Sutera, A. and Vulpiani, A. (1981) The mechanism of stochastic resonance. PMG Report, Department of Computer Science, Chalmers University of Technology, Goteborg, Sweden.Google Scholar
Gammaitoni, L. (1998) Stochastic resonance. Reviews of Modern Physics 70 (2)223–287.Google Scholar
Gang, L. Y., Yong, W. T. and Yan, G. (2007) Study of the property of the parameters of bistable stochastic resonance. Acta Physica Sinica 56 (1)30–34.Google Scholar
Hu, N. Q., Chen, M. and Wen, X. S. (2003) The application of stochastic resonance theory for early detecting rub-impact fault of rotor system. Mechanical Systems and Signal Processing 17 (8)883–895.Google Scholar
Jung, P. and Hanggi, P. (1991) Amplification of small signals via stochastic resonance. Physics Review A 44 (12)8032–8042.Google Scholar
Leng, Y. G. and Wang, T. Y. (2003) Numerical research of twice sampling stochastic resonance for the detection of weak signal submerged in a heavy noise. Acta Physica Sinica 52 (21)2432–2437.Google Scholar
McNamara, B. and Wiesenfeld, K. (1998) Theory of stochastic resonance. Physics Review A 39 (20)4854–4869.Google Scholar
Min, L. and Ying, M. (2010) Frequency coupling in bistable system and the mechanism of stochastic resonance. Acta Physica Sinica 59 (10)3627–3635.Google Scholar
Yang, D. X. and Hu, N. Q. (2004) The Detection of Weak Aperiodic Signal Based on Stochastic Resonance. ISIST2004, Xi'an, China 209–213.Google Scholar