{"title":"一维动力系统的超离散分岔","authors":"S. Ohmori, Y. Yamazaki","doi":"10.1063/5.0012772","DOIUrl":null,"url":null,"abstract":"Bifurcations of one dimensional dynamical systems are discussed based on some ultradiscretized equations.The ultradiscrete equations are derived from the normal forms of one-dimensional nonlinear differential equations,each of which has saddle-node,transcritical,or pitchfork bifurcations. An additional bifurcation, which is similar to flip bifurcation,is also discussed. Dynamical properties of these ultradiscrete bifurcations can be characterized with graphical analysis. As an example of application of our treatment, we focus on an ultradiscrete equation of FitzHugh-Nagumo model, and discuss its dynamical properties.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Ultradiscrete bifurcations for one dimensional dynamical systems\",\"authors\":\"S. Ohmori, Y. Yamazaki\",\"doi\":\"10.1063/5.0012772\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Bifurcations of one dimensional dynamical systems are discussed based on some ultradiscretized equations.The ultradiscrete equations are derived from the normal forms of one-dimensional nonlinear differential equations,each of which has saddle-node,transcritical,or pitchfork bifurcations. An additional bifurcation, which is similar to flip bifurcation,is also discussed. Dynamical properties of these ultradiscrete bifurcations can be characterized with graphical analysis. As an example of application of our treatment, we focus on an ultradiscrete equation of FitzHugh-Nagumo model, and discuss its dynamical properties.\",\"PeriodicalId\":166772,\"journal\":{\"name\":\"arXiv: Chaotic Dynamics\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Chaotic Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0012772\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Chaotic Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/5.0012772","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Ultradiscrete bifurcations for one dimensional dynamical systems
Bifurcations of one dimensional dynamical systems are discussed based on some ultradiscretized equations.The ultradiscrete equations are derived from the normal forms of one-dimensional nonlinear differential equations,each of which has saddle-node,transcritical,or pitchfork bifurcations. An additional bifurcation, which is similar to flip bifurcation,is also discussed. Dynamical properties of these ultradiscrete bifurcations can be characterized with graphical analysis. As an example of application of our treatment, we focus on an ultradiscrete equation of FitzHugh-Nagumo model, and discuss its dynamical properties.
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