{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T13:08:48Z","timestamp":1673615328010},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2014,9,4]],"date-time":"2014-09-04T00:00:00Z","timestamp":1409788800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2014,10]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1017\/s0960129513000716","type":"journal-article","created":{"date-parts":[[2014,9,5]],"date-time":"2014-09-05T00:08:51Z","timestamp":1409875731000},"source":"Crossref","is-referenced-by-count":1,"title":["Dynamic analysis and numerical simulation of a discrete model of a bistable system"],"prefix":"10.1017","volume":"24","author":[{"given":"DINGXIN","family":"YANG","sequence":"first","affiliation":[]},{"given":"ZHENG","family":"HU","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,9,4]]},"reference":[{"key":"S0960129513000716_ref5","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1006\/mssp.2002.1470","article-title":"The application of stochastic resonance theory for early detecting rub-impact fault of rotor system.","volume":"17","author":"Hu","year":"2003","journal-title":"Mechanical Systems and Signal Processing"},{"key":"S0960129513000716_ref4","doi-asserted-by":"crossref","first-page":"30","DOI":"10.7498\/aps.56.30","article-title":"Study of the property of the parameters of bistable stochastic resonance.","volume":"56","author":"Gang","year":"2007","journal-title":"Acta Physica Sinica"},{"key":"S0960129513000716_ref6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.44.8032"},{"key":"S0960129513000716_ref8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.39.4854"},{"key":"S0960129513000716_ref10","unstructured":"Yang D. X. and Hu N. Q. (2004) The Detection of Weak Aperiodic Signal Based on Stochastic Resonance. ISIST2004, Xi'an, China 209\u2013213."},{"key":"S0960129513000716_ref3","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.70.223"},{"key":"S0960129513000716_ref7","doi-asserted-by":"crossref","first-page":"2432","DOI":"10.7498\/aps.52.2432","article-title":"Numerical research of twice sampling stochastic resonance for the detection of weak signal submerged in a heavy noise.","volume":"52","author":"Leng","year":"2003","journal-title":"Acta Physica Sinica"},{"key":"S0960129513000716_ref1","first-page":"1332","article-title":"Detection of weak signals using adaptive stochastic resonance.","volume":"10","author":"Asdi","year":"1995","journal-title":"Acoustics, Speech, and Signal Processing"},{"key":"S0960129513000716_ref9","doi-asserted-by":"crossref","first-page":"3627","DOI":"10.7498\/aps.59.3627","article-title":"Frequency coupling in bistable system and the mechanism of stochastic resonance.","volume":"59","author":"Min","year":"2010","journal-title":"Acta Physica Sinica"},{"key":"S0960129513000716_ref2","doi-asserted-by":"crossref","unstructured":"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.","DOI":"10.1088\/0305-4470\/14\/11\/006"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129513000716","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,16]],"date-time":"2022-04-16T09:24:47Z","timestamp":1650101087000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129513000716\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,4]]},"references-count":10,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["S0960129513000716"],"URL":"https:\/\/doi.org\/10.1017\/s0960129513000716","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,4]]},"article-number":"e240522"}}