Pub Date : 2023-10-04DOI: 10.1080/10236198.2023.2265509
Urszula Bednarz, Małgorzata Wołowiec-Musiał
AbstractIn this paper, by means of independent sets in a graph with multiplicity assigned to each set, we introduce generalized Fibonacci–Leonardo numbers, which are the common generalization of the classical Fibonacci and Leonardo numbers. We give the Binet formula, the generating function, and we prove some identities for generalized Fibonacci–Leonardo numbers. We also define matrix generators for the introduced numbers.Keywords: Fibonacci numbersLeonardo numbersindependent setsmatrix generatorAMS CLASSIFICATIONS: 11B3711B3911C20 AcknowledgmentsThe authors wish to thank the referee for all suggestions which improved this paper.Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"Generalized Fibonacci–Leonardo numbers","authors":"Urszula Bednarz, Małgorzata Wołowiec-Musiał","doi":"10.1080/10236198.2023.2265509","DOIUrl":"https://doi.org/10.1080/10236198.2023.2265509","url":null,"abstract":"AbstractIn this paper, by means of independent sets in a graph with multiplicity assigned to each set, we introduce generalized Fibonacci–Leonardo numbers, which are the common generalization of the classical Fibonacci and Leonardo numbers. We give the Binet formula, the generating function, and we prove some identities for generalized Fibonacci–Leonardo numbers. We also define matrix generators for the introduced numbers.Keywords: Fibonacci numbersLeonardo numbersindependent setsmatrix generatorAMS CLASSIFICATIONS: 11B3711B3911C20 AcknowledgmentsThe authors wish to thank the referee for all suggestions which improved this paper.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135590320","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 : 2023-10-04DOI: 10.1080/10236198.2023.2262613
Peter E. Kloeden, Christian Pötzsche
We consider periodic difference equations in infinite-dimensional Banach spaces possessing compact asymptotically stable set A. It is established that such A persists under spatial discretizations by means of projection methods as nearby closed and bounded uniformly asymptotically stable sets, which moreover converge to A in the Hausdorff metric for increasingly more accurate schemes. The proof is based on a Lyapunov function guaranteed by an ambient converse theorem and a pullback construction. As application serves integrodifference equations on spaces of continuous and p-integrable functions over a compact habitat.
{"title":"Attractive sets of periodic integrodifference equations under discretization","authors":"Peter E. Kloeden, Christian Pötzsche","doi":"10.1080/10236198.2023.2262613","DOIUrl":"https://doi.org/10.1080/10236198.2023.2262613","url":null,"abstract":"We consider periodic difference equations in infinite-dimensional Banach spaces possessing compact asymptotically stable set A. It is established that such A persists under spatial discretizations by means of projection methods as nearby closed and bounded uniformly asymptotically stable sets, which moreover converge to A in the Hausdorff metric for increasingly more accurate schemes. The proof is based on a Lyapunov function guaranteed by an ambient converse theorem and a pullback construction. As application serves integrodifference equations on spaces of continuous and p-integrable functions over a compact habitat.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135596326","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 : 2023-09-29DOI: 10.1080/10236198.2023.2260013
Robert A. Desharnais, Shandelle M. Henson, R. F. Costantino, Brian Dennis
AbstractThe hypothesis of chaotic population dynamics was proposed in ecology by Robert May in the mid-1970s. At that time the idea was controversial, and it remains a fascinating and unsettled issue today. We report the results of a 20-year laboratory research programme that continued in the tradition of the pioneering ecologist Thomas Park using the Tribolium flour beetle model. We present biological evidence of complex population dynamics – including bifurcations, chaos, saddle nodes, phase switching, resonance effects, and multiple attractors – by using a low-dimensional difference equation model for Tribolium together with carefully designed, conducted, and statistically analysed experiments. The model, parameterized with data, also explains the results of historical Tribolium experiments, such as the classical competition studies of Thomas Park and his colleagues. Our research programme has inspired other studies using the Tribolium mathematical and laboratory model. This work was conducted by a multidisciplinary team, which included Jim Cushing.KEYWORDS: Nonlinear dynamicspopulation ecologyTriboliumchaosstochasticity AcknowledgementsWe congratulate Jim on the occasion of his 80th birthday and for his outstanding career. He was a key member of the ‘Beetle Team,’ a multidisciplinary collaborative research group focused on the integration of nonlinear dynamics theory, statistics, and biological experimentation. The members of the Beetle Team were Jim Cushing, R. F. Costantino, Brian Dennis, Robert A. Desharnais, Shandelle M. Henson, Aaron A. King, and Jeffrey Edmunds. We are grateful to the U.S. National Science Foundation, and the American public who support NSF through their taxes, for the opportunity to pursue our passionate desire to strengthen the empirical ties among ecology, statistics, and mathematics.Data availability statementAll of the data from beetle team research programme are publicly available at Dryad in the Beetle Team Tribolium Data Archive: https://doi.org/10.5061/dryad.qjq2bvqmpDisclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe Beetle Team research programme was supported by grants from the U.S. National Science Foundation [grant numbers DMS 9206678, DMS 9306271, DMS 9319073, DMS 9616205, DMS 9625576, DMS 9973126, DMS 9981374, DMS 9981423, DMS 9981458, DMS 0210474].
{"title":"Capturing chaos: a multidisciplinary approach to nonlinear population dynamics","authors":"Robert A. Desharnais, Shandelle M. Henson, R. F. Costantino, Brian Dennis","doi":"10.1080/10236198.2023.2260013","DOIUrl":"https://doi.org/10.1080/10236198.2023.2260013","url":null,"abstract":"AbstractThe hypothesis of chaotic population dynamics was proposed in ecology by Robert May in the mid-1970s. At that time the idea was controversial, and it remains a fascinating and unsettled issue today. We report the results of a 20-year laboratory research programme that continued in the tradition of the pioneering ecologist Thomas Park using the Tribolium flour beetle model. We present biological evidence of complex population dynamics – including bifurcations, chaos, saddle nodes, phase switching, resonance effects, and multiple attractors – by using a low-dimensional difference equation model for Tribolium together with carefully designed, conducted, and statistically analysed experiments. The model, parameterized with data, also explains the results of historical Tribolium experiments, such as the classical competition studies of Thomas Park and his colleagues. Our research programme has inspired other studies using the Tribolium mathematical and laboratory model. This work was conducted by a multidisciplinary team, which included Jim Cushing.KEYWORDS: Nonlinear dynamicspopulation ecologyTriboliumchaosstochasticity AcknowledgementsWe congratulate Jim on the occasion of his 80th birthday and for his outstanding career. He was a key member of the ‘Beetle Team,’ a multidisciplinary collaborative research group focused on the integration of nonlinear dynamics theory, statistics, and biological experimentation. The members of the Beetle Team were Jim Cushing, R. F. Costantino, Brian Dennis, Robert A. Desharnais, Shandelle M. Henson, Aaron A. King, and Jeffrey Edmunds. We are grateful to the U.S. National Science Foundation, and the American public who support NSF through their taxes, for the opportunity to pursue our passionate desire to strengthen the empirical ties among ecology, statistics, and mathematics.Data availability statementAll of the data from beetle team research programme are publicly available at Dryad in the Beetle Team Tribolium Data Archive: https://doi.org/10.5061/dryad.qjq2bvqmpDisclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe Beetle Team research programme was supported by grants from the U.S. National Science Foundation [grant numbers DMS 9206678, DMS 9306271, DMS 9319073, DMS 9616205, DMS 9625576, DMS 9973126, DMS 9981374, DMS 9981423, DMS 9981458, DMS 0210474].","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135193571","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 : 2023-09-26DOI: 10.1080/10236198.2023.2260898
Anna Cima, Armengol Gasull, Víctor Mañosa, Francesc Mañosas
AbstractWe study the dynamics of the piecewise planar rotations Fλ(z)=λ(z−H(z)), with z∈C, H(z)=1 if Im(z)≥0, H(z)=−1 if Im(z)<0, and λ=eiα∈C, being α a rational multiple of π. Our main results establish the dynamics in the so called regular set, which is the complementary of the closure of the set formed by the preimages of the discontinuity line. We prove that any connected component of this set is open, bounded and periodic under the action of Fλ, with a period ℓ, that depends on the connected component. Furthermore, Fλℓ restricted to each component acts as a rotation with a period which also depends on the connected component. As a consequence, any point in the regular set is periodic. Among other results, we also prove that for any connected component of the regular set, its boundary is a convex polygon with certain maximum number of sides.Keywords: Periodic pointspointwise periodic mapspiecewise linear mapsfractal tessellationsMathematics Subject Classifications: 37C2539A2337B10 AcknowledgmentsWe thank our colleague Roser Guardia for the indications regarding the scale factor of the critical set that we mentioned in Section 4.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe first, second and fourth authors are supported by Ministry of Science and Innovation–State Research Agency of the Spanish Government through grants PID2019-104658GB-I00 (first and second authors) and MTM2017-86795-C3-1-P (fourth autor). They are also supported by the grant 2021-SGR-00113 from AGAUR. The second author is supported by grant Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). The third author acknowledges the group research recognition 2021-SGR-01039 from AGAUR.
摘要研究了当z∈C，当Im(z)≥0时H(z)=1，当Im(z)<0时H(z)= - 1，且λ=eiα∈C， α是π的有理倍时，分段平面旋转的动力学。我们的主要结果建立了所谓正则集中的动力学，它是由不连续线的原像形成的集合的闭包的补充。我们证明了在Fλ作用下，这个集合的任何连通分量都是开的、有界的、周期的，其周期取决于连通分量。此外，限制于每个分量的Fλ r作为具有周期的旋转，周期也取决于所连接的分量。因此，正则集中的任何点都是周期性的。在其他结果中，我们还证明了对于正则集的任何连通分量，其边界是一个具有一定最大边数的凸多边形。关键词:周期点-点-周期映射-分段-线性映射-分形曲面关系数学学科分类:37C2539A2337B10致谢我们感谢我们的同事Roser Guardia关于我们在第4节中提到的临界集的比例因子的指示。披露声明作者未报告潜在的利益冲突。论文的第一、二、四作者由西班牙政府科学与创新部国家研究机构资助，资助项目为PID2019-104658GB-I00(第一、二作者)和MTM2017-86795-C3-1-P(第四作者)。他们也得到了AGAUR的2021-SGR-00113基金的支持。第二作者由Severo Ochoa基金和María de Maeztu卓越研发中心和单位计划(CEX2020-001084-M)资助。第三作者感谢AGAUR的小组研究认可2021-SGR-01039。
{"title":"On some rational piecewise linear rotations","authors":"Anna Cima, Armengol Gasull, Víctor Mañosa, Francesc Mañosas","doi":"10.1080/10236198.2023.2260898","DOIUrl":"https://doi.org/10.1080/10236198.2023.2260898","url":null,"abstract":"AbstractWe study the dynamics of the piecewise planar rotations Fλ(z)=λ(z−H(z)), with z∈C, H(z)=1 if Im(z)≥0, H(z)=−1 if Im(z)<0, and λ=eiα∈C, being α a rational multiple of π. Our main results establish the dynamics in the so called regular set, which is the complementary of the closure of the set formed by the preimages of the discontinuity line. We prove that any connected component of this set is open, bounded and periodic under the action of Fλ, with a period ℓ, that depends on the connected component. Furthermore, Fλℓ restricted to each component acts as a rotation with a period which also depends on the connected component. As a consequence, any point in the regular set is periodic. Among other results, we also prove that for any connected component of the regular set, its boundary is a convex polygon with certain maximum number of sides.Keywords: Periodic pointspointwise periodic mapspiecewise linear mapsfractal tessellationsMathematics Subject Classifications: 37C2539A2337B10 AcknowledgmentsWe thank our colleague Roser Guardia for the indications regarding the scale factor of the critical set that we mentioned in Section 4.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe first, second and fourth authors are supported by Ministry of Science and Innovation–State Research Agency of the Spanish Government through grants PID2019-104658GB-I00 (first and second authors) and MTM2017-86795-C3-1-P (fourth autor). They are also supported by the grant 2021-SGR-00113 from AGAUR. The second author is supported by grant Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). The third author acknowledges the group research recognition 2021-SGR-01039 from AGAUR.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134960376","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 : 2023-09-13DOI: 10.1080/10236198.2023.2253329
Laura Gardini, Iryna Sushko, Wirot Tikjha
A one-dimensional rational map f(x)=(x2−a)/(x2−b) depending on the two parameters a and b is considered. Sequences of bifurcations peculiar of rational maps are evidenced, as those occurring due to unbounded cycles (that is, periodic orbits having one point at infinity, related to the vertical asymptotes) that are superstable, as well as to unbounded chaotic intervals. Moreover, two particular bifurcation points, having the role of organizing centres in the (a,b)-parameter plane, are studied. Each point is related to a pair of conditions, which allow us to consider them as the bifurcation points of codimension-2, as it is usual for this kind of organizing centres. However, the two conditions are related not to bifurcations but to degeneracies in the graph of the function. The sequences of bifurcations leading to attracting cycles associated with these particular points are investigated, analytically and numerically, making use of particular properties of the rational map.
{"title":"Dynamics of a rational map: unbounded cycles, unbounded chaotic intervals and organizing centres","authors":"Laura Gardini, Iryna Sushko, Wirot Tikjha","doi":"10.1080/10236198.2023.2253329","DOIUrl":"https://doi.org/10.1080/10236198.2023.2253329","url":null,"abstract":"A one-dimensional rational map f(x)=(x2−a)/(x2−b) depending on the two parameters a and b is considered. Sequences of bifurcations peculiar of rational maps are evidenced, as those occurring due to unbounded cycles (that is, periodic orbits having one point at infinity, related to the vertical asymptotes) that are superstable, as well as to unbounded chaotic intervals. Moreover, two particular bifurcation points, having the role of organizing centres in the (a,b)-parameter plane, are studied. Each point is related to a pair of conditions, which allow us to consider them as the bifurcation points of codimension-2, as it is usual for this kind of organizing centres. However, the two conditions are related not to bifurcations but to degeneracies in the graph of the function. The sequences of bifurcations leading to attracting cycles associated with these particular points are investigated, analytically and numerically, making use of particular properties of the rational map.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135734349","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 : 2023-08-29DOI: 10.1080/10236198.2023.2252712
Published in Journal of Difference Equations and Applications (Vol. 29, No. 7, 2023)
发表于《差分方程与应用》(Vol. 29, No. 7, 2023)
{"title":"Statement of Retraction: on the dynamics of hypersurfaces foliated byn−2-dimensional oriented hyperspheres in Sn","authors":"","doi":"10.1080/10236198.2023.2252712","DOIUrl":"https://doi.org/10.1080/10236198.2023.2252712","url":null,"abstract":"Published in Journal of Difference Equations and Applications (Vol. 29, No. 7, 2023)","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505596","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 : 2023-08-29DOI: 10.1080/10236198.2023.2252717
Published in Journal of Difference Equations and Applications (Vol. 29, No. 7, 2023)
发表于《差分方程与应用》(Vol. 29, No. 7, 2023)
{"title":"Statement of retraction: A generalized real option pricing method of R&D investments: jump diffusion and external competition","authors":"","doi":"10.1080/10236198.2023.2252717","DOIUrl":"https://doi.org/10.1080/10236198.2023.2252717","url":null,"abstract":"Published in Journal of Difference Equations and Applications (Vol. 29, No. 7, 2023)","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543489","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 : 2023-08-25DOI: 10.1080/10236198.2023.2249129
H. Thieme
{"title":"Continuity of the spectral radius, applied to structured semelparous two-sex population models","authors":"H. Thieme","doi":"10.1080/10236198.2023.2249129","DOIUrl":"https://doi.org/10.1080/10236198.2023.2249129","url":null,"abstract":"","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80754293","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 : 2023-08-03DOI: 10.1080/10236198.2023.2263094
Yaling Shi, Kesong Yan, Fanping Zeng
AbstractBased on the preimage structure of the system (X,T), Hurley introduced the notion of pointwise topological preimage entropies hm(T) and hp(T). Furthermore, from the measure-theoretic point of view, Wu and Zhu introduced a notion of pointwise metric preimage entropy hm,μ(T) for a T-invariant measure µ on X, and obtained the variational principle between hm,μ(T) and hm(T) under the condition of uniform separation of preimages. A natural question is whether a variational principle for hm(T) and hm,μ(T) without any additional assumptions. In this paper, we define a new version of topological preimage entropy hm(T|μ) relative to a T-invariant measure µ, and show that the inequality hm,μ(T)⩽hm(T|μ)⩽hp(T) holds for every T-invariant probability measure µ. As a consequence, we obtain that there is a topological dynamical system (X,T) such that the following strict inequality holds: supμ∈M(X,T)hm,μ(T)
{"title":"Variational principles for pointwise preimage entropies","authors":"Yaling Shi, Kesong Yan, Fanping Zeng","doi":"10.1080/10236198.2023.2263094","DOIUrl":"https://doi.org/10.1080/10236198.2023.2263094","url":null,"abstract":"AbstractBased on the preimage structure of the system (X,T), Hurley introduced the notion of pointwise topological preimage entropies hm(T) and hp(T). Furthermore, from the measure-theoretic point of view, Wu and Zhu introduced a notion of pointwise metric preimage entropy hm,μ(T) for a T-invariant measure µ on X, and obtained the variational principle between hm,μ(T) and hm(T) under the condition of uniform separation of preimages. A natural question is whether a variational principle for hm(T) and hm,μ(T) without any additional assumptions. In this paper, we define a new version of topological preimage entropy hm(T|μ) relative to a T-invariant measure µ, and show that the inequality hm,μ(T)⩽hm(T|μ)⩽hp(T) holds for every T-invariant probability measure µ. As a consequence, we obtain that there is a topological dynamical system (X,T) such that the following strict inequality holds: supμ∈M(X,T)hm,μ(T)<hm(T),where M(X,T) denote the set of all T-invariant probability measures.Keywords: Preimage entropyvariational principlenon-invertible map2000 Mathematics Subject Classifications: Primary: 37A25Secondary: 37A3537A05 AcknowledgmentsThe authors would like to thank the anonymous referees for their useful comments and helpful suggestions that improved the manuscript. We also thank Jiehua Mai for the careful reading and helpful suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe authors are supported by NNSF of China (12261006) and NSF of Guangxi Province (2018GXNSFFA281008). The second author is also supported by NNSF of China (12171175) and Project of First Class Disciplines of Statistics of Guangxi Province.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136383346","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 : 2023-08-03DOI: 10.1080/10236198.2023.2254625
{"title":"Correction Statement","authors":"","doi":"10.1080/10236198.2023.2254625","DOIUrl":"https://doi.org/10.1080/10236198.2023.2254625","url":null,"abstract":"","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136382140","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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