{"title":"关于差分方程的定性行为 $\\delta _{m+1}=\\omega +\\zeta \\frac{f(\\delta _{m},\\delta _{m-1})}{\\delta _{m-1}^{\\beta}}$","authors":"M. Gümüş, Şeyma Irmak Eği̇lmez","doi":"10.36753/mathenot.1243583","DOIUrl":null,"url":null,"abstract":"In this paper, we aim to investigate the qualitative behavior of a general class of non-linear difference equations. That is, the prime period two solutions, the prime period three solutions and the stability character are examined. We also use a new technique introduced in [1] by E. M. Elsayed and later developed by O. Moaaz in [2] to examine the existence of periodic solutions of these general equations. Moreover, we use homogeneous functions for the investigation of the dynamics of the aforementioned equations.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Qualitative Behavior of the Difference Equation $\\\\delta _{m+1}=\\\\omega +\\\\zeta \\\\frac{f(\\\\delta _{m},\\\\delta _{m-1})}{\\\\delta _{m-1}^{\\\\beta}}$\",\"authors\":\"M. Gümüş, Şeyma Irmak Eği̇lmez\",\"doi\":\"10.36753/mathenot.1243583\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we aim to investigate the qualitative behavior of a general class of non-linear difference equations. That is, the prime period two solutions, the prime period three solutions and the stability character are examined. We also use a new technique introduced in [1] by E. M. Elsayed and later developed by O. Moaaz in [2] to examine the existence of periodic solutions of these general equations. Moreover, we use homogeneous functions for the investigation of the dynamics of the aforementioned equations.\",\"PeriodicalId\":127589,\"journal\":{\"name\":\"Mathematical Sciences and Applications E-Notes\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-03-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Sciences and Applications E-Notes\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.36753/mathenot.1243583\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Sciences and Applications E-Notes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.36753/mathenot.1243583","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文的目的是研究一类一般非线性差分方程的定性性质。即对素数周期二解、素数周期三解及其稳定性进行了研究。我们还使用E. M. Elsayed在[1]中引入的一种新技术,后来由O. Moaaz在[2]中发展起来,来检验这些一般方程周期解的存在性。此外,我们使用齐次函数来研究上述方程的动力学。
On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$
In this paper, we aim to investigate the qualitative behavior of a general class of non-linear difference equations. That is, the prime period two solutions, the prime period three solutions and the stability character are examined. We also use a new technique introduced in [1] by E. M. Elsayed and later developed by O. Moaaz in [2] to examine the existence of periodic solutions of these general equations. Moreover, we use homogeneous functions for the investigation of the dynamics of the aforementioned equations.