{"title":"BURSTING SOLUTIONS OF THE RÖSSLER EQUATIONS","authors":"A. Fowler, M. Mcguinness","doi":"10.1017/S144618112300010X","DOIUrl":null,"url":null,"abstract":"Abstract We provide an analytic solution of the Rössler equations based on the asymptotic limit \n$c\\to \\infty $\n and we show in this limit that the solution takes the form of multiple pulses, similar to “burst” firing of neurons. We are able to derive an approximate Poincaré map for the solutions, which compares reasonably with a numerically derived map.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"76 1","pages":"93 - 110"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The ANZIAM journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/S144618112300010X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract We provide an analytic solution of the Rössler equations based on the asymptotic limit
$c\to \infty $
and we show in this limit that the solution takes the form of multiple pulses, similar to “burst” firing of neurons. We are able to derive an approximate Poincaré map for the solutions, which compares reasonably with a numerically derived map.
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