{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T07:43:19Z","timestamp":1753602199681,"version":"3.37.3"},"reference-count":38,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11202120"],"award-info":[{"award-number":["11202120"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["GK201502007","GK201701001"],"award-info":[{"award-number":["GK201502007","GK201701001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,12,15]]},"abstract":"<jats:p>We aim to investigate bifurcation behaviors in a stochastic birhythmic van der Pol (BVDP) system subjected to delay self-control feedback. First, the harmonic approximation is adopted to drive the delay self-control feedback to state variables without delay. Then, Fokker\u2013Planck\u2013Kolmogorov (FPK) equation and stationary probability density function (SPDF) for amplitude are obtained by applying stochastic averaging method. Finally, dynamical scenarios of the change of delay self-control feedback as well as noise that markedly influence bifurcation performance are observed. It is found that: the big feedback strength and delay will suppress the large amplitude limit cycle (LC) while the relatively big noise strength facilitates the large amplitude LC, which imply the proposed regulation strategies are feasible. Interestingly enough, the inner LC is never destroyed due to noise. Furthermore, the validity of analytical results was verified by Monte Carlo simulation of the dynamics.<\/jats:p>","DOI":"10.1142\/s0218127417502029","type":"journal-article","created":{"date-parts":[[2018,1,3]],"date-time":"2018-01-03T08:03:43Z","timestamp":1514966623000},"page":"1750202","source":"Crossref","is-referenced-by-count":9,"title":["Bifurcation Regulations Governed by Delay Self-Control Feedback in a Stochastic Birhythmic System"],"prefix":"10.1142","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9213-2013","authenticated-orcid":false,"given":"Zhidan","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an 710119, P. R. China"}]},{"given":"Lijuan","family":"Ning","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an 710119, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2018,1,3]]},"reference":[{"key":"S0218127417502029BIB001","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0017075"},{"key":"S0218127417502029BIB002","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.94.042226"},{"key":"S0218127417502029BIB003","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjp\/i2012-12001-7","volume":"127","author":"Chamgou\u00e9 A. C.","year":"2012","journal-title":"Eur. Phys. J. Plus"},{"key":"S0218127417502029BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-013-0931-7"},{"key":"S0218127417502029BIB005","first-page":"517","volume":"27","author":"Chen L. C.","year":"2010","journal-title":"Chinese J. Appl. Mech."},{"key":"S0218127417502029BIB006","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.79.22.6917"},{"key":"S0218127417502029BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00419-012-0623-7"},{"key":"S0218127417502029BIB008","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.64.021917"},{"key":"S0218127417502029BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416501029"},{"key":"S0218127417502029BIB010","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.83.036205"},{"key":"S0218127417502029BIB011","doi-asserted-by":"publisher","DOI":"10.1038\/nature01259"},{"key":"S0218127417502029BIB012","first-page":"1466","volume":"60","author":"Gu R. C.","year":"2011","journal-title":"Acta Phys. Sin."},{"key":"S0218127417502029BIB013","first-page":"257","volume":"45","author":"Hao Y.","year":"2013","journal-title":"Chinese J. Theoret. Appl. Mech."},{"key":"S0218127417502029BIB014","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.92.050601"},{"key":"S0218127417502029BIB015","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1515\/znc-1978-3-422","volume":"33","author":"Kaiser F.","year":"1978","journal-title":"Z. Naturforsch. A"},{"key":"S0218127417502029BIB016","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.76.035201"},{"key":"S0218127417502029BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/0266-8920(86)90006-8"},{"key":"S0218127417502029BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2015.08.036"},{"key":"S0218127417502029BIB019","doi-asserted-by":"publisher","DOI":"10.1109\/JQE.2002.805110"},{"key":"S0218127417502029BIB020","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.68.066211"},{"key":"S0218127417502029BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(92)90745-8"},{"key":"S0218127417502029BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7462(86)90025-9"},{"key":"S0218127417502029BIB023","first-page":"32","volume":"18","author":"Rong H. W.","year":"2001","journal-title":"Chinese J. Appl. Mech."},{"key":"S0218127417502029BIB024","doi-asserted-by":"publisher","DOI":"10.1038\/439027a"},{"key":"S0218127417502029BIB025","doi-asserted-by":"publisher","DOI":"10.1063\/1.4927646"},{"key":"S0218127417502029BIB026","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404010990"},{"key":"S0218127417502029BIB027","doi-asserted-by":"publisher","DOI":"10.1115\/1.2948382"},{"key":"S0218127417502029BIB028","first-page":"524","volume":"43","author":"Wu Z. Q.","year":"2013","journal-title":"Sci. Sin."},{"key":"S0218127417502029BIB029","doi-asserted-by":"crossref","first-page":"060501","DOI":"10.7498\/aps.64.060501","volume":"64","author":"Wu Z. Q.","year":"2015","journal-title":"Acta Phys. Sin."},{"key":"S0218127417502029BIB030","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1994.1294"},{"key":"S0218127417502029BIB031","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404010989"},{"key":"S0218127417502029BIB032","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.83.056215"},{"key":"S0218127417502029BIB033","doi-asserted-by":"publisher","DOI":"10.1063\/1.4766678"},{"key":"S0218127417502029BIB034","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.81.011106"},{"key":"S0218127417502029BIB035","doi-asserted-by":"publisher","DOI":"10.2478\/amcs-2014-0063"},{"key":"S0218127417502029BIB036","unstructured":"Zhu, W. Q. [1988] Random Vibration (Beijing Science Press, Beijing), pp. 492\u2013523."},{"key":"S0218127417502029BIB037","doi-asserted-by":"publisher","DOI":"10.1007\/BF02487660"},{"key":"S0218127417502029BIB038","doi-asserted-by":"publisher","DOI":"10.1115\/1.3101980"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417502029","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T18:46:14Z","timestamp":1660243574000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417502029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,15]]},"references-count":38,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2018,1,3]]},"published-print":{"date-parts":[[2017,12,15]]}},"alternative-id":["10.1142\/S0218127417502029"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417502029","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2017,12,15]]}}}