{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T01:44:36Z","timestamp":1778031876452,"version":"3.51.4"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"15","funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2020YJS175"],"award-info":[{"award-number":["2020YJS175"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,12,15]]},"abstract":"<jats:p>The existence of chaos in the Rulkov neuron model is proved based on Marotto\u2019s theorem. Firstly, the stability conditions of the model are briefly renewed through analyzing the eigenvalues of the model, which are very important preconditions for the existence of a snap-back repeller. Secondly, the Rulkov neuron model is decomposed to a one-dimensional fast subsystem and a one-dimensional slow subsystem by the fast\u2013slow dynamics technique, in which the fast subsystem has sensitive dependence on the initial conditions and its snap-back repeller and chaos can be verified by numerical methods, such as waveforms, Lyapunov exponents, and bifurcation diagrams. Thirdly, for the two-dimensional Rulkov neuron model, it is proved that there exists a snap-back repeller under two iterations by illustrating the existence of an intersection of three surfaces, which pave a new way to identify the existence of a snap-back repeller.<\/jats:p>","DOI":"10.1142\/s0218127421502333","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T11:30:05Z","timestamp":1638876605000},"source":"Crossref","is-referenced-by-count":5,"title":["Chaos in the Rulkov Neuron Model Based on Marotto\u2019s Theorem"],"prefix":"10.1142","volume":"31","author":[{"given":"Penghe","family":"Ge","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4625-5351","authenticated-orcid":false,"given":"Hongjun","family":"Cao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,12,7]]},"reference":[{"key":"S0218127421502333BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s10339-008-0222-2"},{"key":"S0218127421502333BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413300413"},{"key":"S0218127421502333BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127417501784"},{"key":"S0218127421502333BIB004","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.64.051914"},{"key":"S0218127421502333BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s10255-014-0435-3"},{"key":"S0218127421502333BIB007","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.77.051918"},{"key":"S0218127421502333BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2010.12.003"},{"key":"S0218127421502333BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412500678"},{"key":"S0218127421502333BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2003.12.043"},{"key":"S0218127421502333BIB011","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1975.11994008"},{"key":"S0218127421502333BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2019.03.017"},{"key":"S0218127421502333BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(78)90115-4"},{"key":"S0218127421502333BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.10.003"},{"key":"S0218127421502333BIB015","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.86.183"},{"key":"S0218127421502333BIB016","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.65.041922"},{"key":"S0218127421502333BIB017","doi-asserted-by":"publisher","DOI":"10.1063\/1.4964981"},{"key":"S0218127421502333BIB018","doi-asserted-by":"crossref","first-page":"120502","DOI":"10.7498\/aps.65.120502","volume":"65","author":"Sun X.","year":"2016","journal-title":"Acta Phys. Sin."},{"key":"S0218127421502333BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2013.01.026"},{"key":"S0218127421502333BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2013.10.004"},{"key":"S0218127421502333BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2014.06.015"},{"key":"S0218127421502333BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4067-7"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127421502333","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T14:45:04Z","timestamp":1673966704000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127421502333"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,7]]},"references-count":21,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2021,12,15]]}},"alternative-id":["10.1142\/S0218127421502333"],"URL":"https:\/\/doi.org\/10.1142\/s0218127421502333","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,7]]},"article-number":"2150233"}}