Pub Date : 2023-11-27DOI: 10.1080/10236198.2023.2284832
Hafedh Abdelli, Ghassen Askri
Let X be a local dendrite and let f:X→X be a continuous map. Denote by P(f) and R(f) the sets of periodic and recurrent points of f, respectively. We say that f is relatively pointwise recurrent if...
{"title":"Relatively pointwise recurrence on local dendrites","authors":"Hafedh Abdelli, Ghassen Askri","doi":"10.1080/10236198.2023.2284832","DOIUrl":"https://doi.org/10.1080/10236198.2023.2284832","url":null,"abstract":"Let X be a local dendrite and let f:X→X be a continuous map. Denote by P(f) and R(f) the sets of periodic and recurrent points of f, respectively. We say that f is relatively pointwise recurrent if...","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"501 ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.1080/10236198.2023.2284827
U. U. Jamilov, Kh. O. Khudoyberdiev
The present paper deals to a family of non-Volterra quadratic stochastic operators depending on a parameter and a permutation and their trajectory behaviours. We find all fixed and periodic points ...
本文研究了一类非volterra二次型随机算子及其轨迹行为。我们找到了所有的固定点和周期点。
{"title":"On the dynamics of non-Volterra quadratic operators corresponding to permutations","authors":"U. U. Jamilov, Kh. O. Khudoyberdiev","doi":"10.1080/10236198.2023.2284827","DOIUrl":"https://doi.org/10.1080/10236198.2023.2284827","url":null,"abstract":"The present paper deals to a family of non-Volterra quadratic stochastic operators depending on a parameter and a permutation and their trajectory behaviours. We find all fixed and periodic points ...","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"508 ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.1080/10236198.2023.2285394
Janusz Mierczyński, Stephen Baigent
We present a dynamical approach to the study of unordered, attracting manifolds of retrotone maps commonly known as carrying simplices. Our approach is novel in that it uses the radial representati...
{"title":"Existence of the carrying simplex for a retrotone map","authors":"Janusz Mierczyński, Stephen Baigent","doi":"10.1080/10236198.2023.2285394","DOIUrl":"https://doi.org/10.1080/10236198.2023.2285394","url":null,"abstract":"We present a dynamical approach to the study of unordered, attracting manifolds of retrotone maps commonly known as carrying simplices. Our approach is novel in that it uses the radial representati...","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"511 ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-23DOI: 10.1080/10236198.2023.2284829
George Spahn, Doron Zeilberger
We demonstrate the power of Experimental Mathematics and Symbolic Computation to study intriguing problems on rational difference equations, studied extensively by Difference Equations giants, Sabe...
{"title":"Experimenting with discrete dynamical systems","authors":"George Spahn, Doron Zeilberger","doi":"10.1080/10236198.2023.2284829","DOIUrl":"https://doi.org/10.1080/10236198.2023.2284829","url":null,"abstract":"We demonstrate the power of Experimental Mathematics and Symbolic Computation to study intriguing problems on rational difference equations, studied extensively by Difference Equations giants, Sabe...","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"491 ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-21DOI: 10.1080/10236198.2023.2281552
Saber Elaydi, Yun Kang, Rafael Luís
This paper is dedicated to Jim Cushing on the occasion of his 80th birthday. It is inspired by his work on evolutionary theory. We investigate the global dynamics of discrete-time phenotypic evolut...
{"title":"Global asymptotic stability of evolutionary periodic Ricker competition models","authors":"Saber Elaydi, Yun Kang, Rafael Luís","doi":"10.1080/10236198.2023.2281552","DOIUrl":"https://doi.org/10.1080/10236198.2023.2281552","url":null,"abstract":"This paper is dedicated to Jim Cushing on the occasion of his 80th birthday. It is inspired by his work on evolutionary theory. We investigate the global dynamics of discrete-time phenotypic evolut...","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"19 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-20DOI: 10.1080/10236198.2023.2284831
Mario Lefebvre
Let (Xn,Yn) be a two-dimensional discrete-time controlled Markov chain. The problem of optimally controlling the chain until the sum Xn+Yn is equal to either of two constants is considered. The aim...
{"title":"Controlled two-dimensional Markov chains between two absorbing barriers","authors":"Mario Lefebvre","doi":"10.1080/10236198.2023.2284831","DOIUrl":"https://doi.org/10.1080/10236198.2023.2284831","url":null,"abstract":"Let (Xn,Yn) be a two-dimensional discrete-time controlled Markov chain. The problem of optimally controlling the chain until the sum Xn+Yn is equal to either of two constants is considered. The aim...","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"20 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-20DOI: 10.1080/10236198.2023.2284195
Chuanan Wei
Let β(z) be the Dirichlet beta function. Series for β(4) are very rare in the historical development of mathematics. With the help of the operator method and a transformation formula for hypergeome...
{"title":"On a conjectural series of Sun for the mathematical constant β(4)","authors":"Chuanan Wei","doi":"10.1080/10236198.2023.2284195","DOIUrl":"https://doi.org/10.1080/10236198.2023.2284195","url":null,"abstract":"Let β(z) be the Dirichlet beta function. Series for β(4) are very rare in the historical development of mathematics. With the help of the operator method and a transformation formula for hypergeome...","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"19 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-16DOI: 10.1080/10236198.2023.2267824
René Lozi, Lyudmila Efremova, Mohammed-Salah Abdelouahab, Safwan El Assad, Michal Pluhacek
This foreword presents the 32 articles of the special issue devoted to the Lozi, Hénon and other chaotic attractors proposed by 78 authors from 20 countries (Algeria, Brazil, Canada, China, Czech R...
{"title":"Foreword to the special issue of Journal of Difference Equations and Applications on ‘Lozi, Hénon, and other chaotic attractors, theory and applications’","authors":"René Lozi, Lyudmila Efremova, Mohammed-Salah Abdelouahab, Safwan El Assad, Michal Pluhacek","doi":"10.1080/10236198.2023.2267824","DOIUrl":"https://doi.org/10.1080/10236198.2023.2267824","url":null,"abstract":"This foreword presents the 32 articles of the special issue devoted to the Lozi, Hénon and other chaotic attractors proposed by 78 authors from 20 countries (Algeria, Brazil, Canada, China, Czech R...","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"20 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.1080/10236198.2023.2280241
Xu Zhang
AbstractA generalized family of transcendental (non-polynomial entire) functions is constructed, where the Hausdorff dimension and the packing dimension of the Julia sets are equal to one. Further, there exist multiply connected wandering domains, the dynamics can be completed described, and for any s∈(0,+∞], there is a function taken from this family with the order of growth s. Baker proved that the Hausdorff dimension of a transcendental function is no less than one in 1975, the minimum value was obtained via an elegant construction by Bishop in 2018. The order of growth is zero in Bishop's construction, the family of functions here have arbitrarily positive or even infinite order of growth.Keywords: Fatou setHausdorff dimensionJulia setpacking dimensiontranscendental function2020 Mathematics Subject Classifications: 37F1030D0537F3537C45 AcknowledgementsThe authors appreciate Prof. Christopher Bishop, whose continuous encouragement and support made it possible to finish this work. The authors also appreciate the anonymous reviewers for their helpful comments and suggestions, which improve the manuscript greatly.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by the Shandong Provincial Natural Science Foundation, China [grant number ZR2023MA047].
{"title":"A generalized family of transcendental functions with one dimensional Julia sets","authors":"Xu Zhang","doi":"10.1080/10236198.2023.2280241","DOIUrl":"https://doi.org/10.1080/10236198.2023.2280241","url":null,"abstract":"AbstractA generalized family of transcendental (non-polynomial entire) functions is constructed, where the Hausdorff dimension and the packing dimension of the Julia sets are equal to one. Further, there exist multiply connected wandering domains, the dynamics can be completed described, and for any s∈(0,+∞], there is a function taken from this family with the order of growth s. Baker proved that the Hausdorff dimension of a transcendental function is no less than one in 1975, the minimum value was obtained via an elegant construction by Bishop in 2018. The order of growth is zero in Bishop's construction, the family of functions here have arbitrarily positive or even infinite order of growth.Keywords: Fatou setHausdorff dimensionJulia setpacking dimensiontranscendental function2020 Mathematics Subject Classifications: 37F1030D0537F3537C45 AcknowledgementsThe authors appreciate Prof. Christopher Bishop, whose continuous encouragement and support made it possible to finish this work. The authors also appreciate the anonymous reviewers for their helpful comments and suggestions, which improve the manuscript greatly.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by the Shandong Provincial Natural Science Foundation, China [grant number ZR2023MA047].","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"23 17","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136281965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-09DOI: 10.1080/10236198.2023.2279628
Bo Zheng, Jianshe Yu
AbstractIn this paper, we establish a discrete model with periodic parameters to depict the Wolbachia spread dynamics in mosquito populations in cyclic environments. This work modifies the models established in the existing literature that did not take into account the variation of parameters with environmental periodic changes due to seasonality and other factors. When the parameters in our model are constants, it has been extensively studied and widely used. We present a conjecture about the existence of at most two periodic solutions worthy of further study, and show that the conjecture is true for the special case of 2-periodic parameters. Numerical simulations are also provided to illustrate the occurrence of periodic phenomena.Keywords: Mosquito-borne diseasesWolbachianon-autonomous discrete modelperiodic solutionscyclic environmentsMSC(2020):: 92B0592D3037N25 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by National Natural Science Foundation of China (Nos: 11971127, 12331017, 12071095, 12371484).
{"title":"<i>Wolbachia</i> spread dynamics in mosquito populations in cyclic environments","authors":"Bo Zheng, Jianshe Yu","doi":"10.1080/10236198.2023.2279628","DOIUrl":"https://doi.org/10.1080/10236198.2023.2279628","url":null,"abstract":"AbstractIn this paper, we establish a discrete model with periodic parameters to depict the Wolbachia spread dynamics in mosquito populations in cyclic environments. This work modifies the models established in the existing literature that did not take into account the variation of parameters with environmental periodic changes due to seasonality and other factors. When the parameters in our model are constants, it has been extensively studied and widely used. We present a conjecture about the existence of at most two periodic solutions worthy of further study, and show that the conjecture is true for the special case of 2-periodic parameters. Numerical simulations are also provided to illustrate the occurrence of periodic phenomena.Keywords: Mosquito-borne diseasesWolbachianon-autonomous discrete modelperiodic solutionscyclic environmentsMSC(2020):: 92B0592D3037N25 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by National Natural Science Foundation of China (Nos: 11971127, 12331017, 12071095, 12371484).","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":" 19","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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