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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: yangdingxincn@163.com; huzheng@nudt.edu.cn
ZHENG HU
Affiliation:
College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha, China Email: yangdingxincn@163.com; huzheng@nudt.edu.cn
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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.

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