{"title":"包含指数项的差分方程的动态行为和分岔分析","authors":"A. A. Elsadany, Samia Ibrahim, E. Elabbasy","doi":"10.28919/cpr-pajm/3-14","DOIUrl":null,"url":null,"abstract":"In this paper, the local stability, the boundedness, rate of convergence and the conditions of Neimark-Sacker bifurcation concerning difference equationxn+1=α1xn+α2xn-1+β1xnexp(-x2n-1)+β2xn-1exp(-x2n-1), n=0,1, ...,are investigated. We focus on the Neimark-Sacker bifurcations of the discrete model. The center manifold theorem and bifurcation theory are explicitly applied to reach conclusions about the occurrence and stability of the Neimark-Sacker bifurcation. Many numerical simulations that confirm the existence of the Neimark-Sacker bifurcation are also provided.","PeriodicalId":503253,"journal":{"name":"Pan-American Journal of Mathematics","volume":"66 5","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamic Behavior and Bifurcation Analysis of a Difference Equation Including Exponential Terms\",\"authors\":\"A. A. Elsadany, Samia Ibrahim, E. Elabbasy\",\"doi\":\"10.28919/cpr-pajm/3-14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the local stability, the boundedness, rate of convergence and the conditions of Neimark-Sacker bifurcation concerning difference equationxn+1=α1xn+α2xn-1+β1xnexp(-x2n-1)+β2xn-1exp(-x2n-1), n=0,1, ...,are investigated. We focus on the Neimark-Sacker bifurcations of the discrete model. The center manifold theorem and bifurcation theory are explicitly applied to reach conclusions about the occurrence and stability of the Neimark-Sacker bifurcation. Many numerical simulations that confirm the existence of the Neimark-Sacker bifurcation are also provided.\",\"PeriodicalId\":503253,\"journal\":{\"name\":\"Pan-American Journal of Mathematics\",\"volume\":\"66 5\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pan-American Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.28919/cpr-pajm/3-14\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pan-American Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.28919/cpr-pajm/3-14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Dynamic Behavior and Bifurcation Analysis of a Difference Equation Including Exponential Terms
In this paper, the local stability, the boundedness, rate of convergence and the conditions of Neimark-Sacker bifurcation concerning difference equationxn+1=α1xn+α2xn-1+β1xnexp(-x2n-1)+β2xn-1exp(-x2n-1), n=0,1, ...,are investigated. We focus on the Neimark-Sacker bifurcations of the discrete model. The center manifold theorem and bifurcation theory are explicitly applied to reach conclusions about the occurrence and stability of the Neimark-Sacker bifurcation. Many numerical simulations that confirm the existence of the Neimark-Sacker bifurcation are also provided.
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