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.
{"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":"https://doi.org/10.28919/cpr-pajm/3-14","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":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141346604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce the two-wavelet multiplier operator in the Laguerre hypergroup setting. Knowing the fact that the study of this operator are both theoretically interesting and practically useful, we investigated several subjects of spectral analysis for the new operator. Firstly, we present a comprehensive analysis of the generalized two-wavelet multiplier operator. Next, we introduce and we study the generalized Landau-PollakSlepian operator. As applications, some problems of the approximation theory and the uncertainty principles are studied. Finally, we give many results on the boundedness and compactness of the Laguerre two-wavelet multipliers on Lpα(K), 1≤p≤∞.
{"title":"Spectral Theorems in the Laguerre Hypergroup Setting","authors":"H. Mejjaoli, Firdous A. Shah","doi":"10.28919/cpr-pajm/3-13","DOIUrl":"https://doi.org/10.28919/cpr-pajm/3-13","url":null,"abstract":"We introduce the two-wavelet multiplier operator in the Laguerre hypergroup setting. Knowing the fact that the study of this operator are both theoretically interesting and practically useful, we investigated several subjects of spectral analysis for the new operator. Firstly, we present a comprehensive analysis of the generalized two-wavelet multiplier operator. Next, we introduce and we study the generalized Landau-PollakSlepian operator. As applications, some problems of the approximation theory and the uncertainty principles are studied. Finally, we give many results on the boundedness and compactness of the Laguerre two-wavelet multipliers on Lpα(K), 1≤p≤∞.","PeriodicalId":503253,"journal":{"name":"Pan-American Journal of Mathematics","volume":"48 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141111369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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