Pub Date : 2023-08-03DOI: 10.1080/10236198.2023.2255308
Jianxi Mao, Yanni Pei
We present sufficient conditions for the asymptotic log-convexity of Apéry-like numbers which satisfy three-term recursions. Our techniques are based on the famous Birkhoff–Adams theorem.
{"title":"The asymptotic log-convexity of Apéry-like numbers","authors":"Jianxi Mao, Yanni Pei","doi":"10.1080/10236198.2023.2255308","DOIUrl":"https://doi.org/10.1080/10236198.2023.2255308","url":null,"abstract":"We present sufficient conditions for the asymptotic log-convexity of Apéry-like numbers which satisfy three-term recursions. Our techniques are based on the famous Birkhoff–Adams theorem.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"106 1","pages":"799 - 813"},"PeriodicalIF":1.1,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75796847","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 : 2023-07-24DOI: 10.1080/10236198.2023.2236728
B. Coomes, H. Koçak, K. Palmer
{"title":"Homoclinic chaos in a perennial grass model","authors":"B. Coomes, H. Koçak, K. Palmer","doi":"10.1080/10236198.2023.2236728","DOIUrl":"https://doi.org/10.1080/10236198.2023.2236728","url":null,"abstract":"","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"9 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80177016","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 : 2023-07-05DOI: 10.1080/10236198.2023.2228926
R. Lozi
{"title":"Research on actual or industrial applications of difference equations: a chimerical task?","authors":"R. Lozi","doi":"10.1080/10236198.2023.2228926","DOIUrl":"https://doi.org/10.1080/10236198.2023.2228926","url":null,"abstract":"","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"11 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89391686","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 : 2023-07-03DOI: 10.1080/10236198.2023.2253327
T. Mansour
An inversion sequence of length n is a word which satisfies for each the inequalities . In this paper, we present enumerations of four classes of inversion sequences that avoid a pattern of length 4. More precisely, we describe each class by a generating tree with 2 labels, and then we obtain an explicit formula for the generating function for the number of inversion sequences of length n that avoid either 0132, , , 0123, or 0321.
{"title":"Five classes of pattern avoiding inversion sequences under one roof: generating trees","authors":"T. Mansour","doi":"10.1080/10236198.2023.2253327","DOIUrl":"https://doi.org/10.1080/10236198.2023.2253327","url":null,"abstract":"An inversion sequence of length n is a word which satisfies for each the inequalities . In this paper, we present enumerations of four classes of inversion sequences that avoid a pattern of length 4. More precisely, we describe each class by a generating tree with 2 labels, and then we obtain an explicit formula for the generating function for the number of inversion sequences of length n that avoid either 0132, , , 0123, or 0321.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"53 1","pages":"748 - 762"},"PeriodicalIF":1.1,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90680047","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 : 2023-06-28DOI: 10.1080/10236198.2023.2220416
I. Zelinka, R. Šenkeřík
This paper delves into the intersection between discrete dynamical systems and bio-inspired metaheuristic algorithms. Chaos, an inherent phenomenon manifested by both continuous and discrete dynamic nonlinear systems has become an essential component of engineering design. This study examines the relationship between chaos and bio-inspired metaheuristic algorithms from two distinct angles: the presence of chaos within the realm of algorithms, and the application of bio-inspired algorithms for the identification, control, or synthesis of complex systems. Furthermore, this paper offers an in-depth exploration of the interplay between metaheuristics and complex nonlinear dynamics, including potential avenues for future research. The presented simulation studies, along with the design of objective functions for optimization and the implementation of metaheuristics, serve as a valuable foundation for subsequent experiments involving discrete nonlinear systems and complex systems with time delays. Such systems may benefit from multiparametric or multicriteria optimization approaches, paving the way for novel advancements in the field.
{"title":"Chaotic attractors of discrete dynamical systems used in the core of evolutionary algorithms: state of art and perspectives","authors":"I. Zelinka, R. Šenkeřík","doi":"10.1080/10236198.2023.2220416","DOIUrl":"https://doi.org/10.1080/10236198.2023.2220416","url":null,"abstract":"This paper delves into the intersection between discrete dynamical systems and bio-inspired metaheuristic algorithms. Chaos, an inherent phenomenon manifested by both continuous and discrete dynamic nonlinear systems has become an essential component of engineering design. This study examines the relationship between chaos and bio-inspired metaheuristic algorithms from two distinct angles: the presence of chaos within the realm of algorithms, and the application of bio-inspired algorithms for the identification, control, or synthesis of complex systems. Furthermore, this paper offers an in-depth exploration of the interplay between metaheuristics and complex nonlinear dynamics, including potential avenues for future research. The presented simulation studies, along with the design of objective functions for optimization and the implementation of metaheuristics, serve as a valuable foundation for subsequent experiments involving discrete nonlinear systems and complex systems with time delays. Such systems may benefit from multiparametric or multicriteria optimization approaches, paving the way for novel advancements in the field.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"149 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86124794","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 : 2023-06-26DOI: 10.1080/10236198.2023.2228421
Habiba Meskine, Mohammed Salah Abdelouahab, R. Lozi
The purpose of this paper is to investigate the dynamics of a remanufacturing duopoly game model with heterogeneous players and different competition strategies, assuming that the original equipment manufacturer has bounded rationality and aims to maximize profit, and the third-party remanufacturer has an adaptive nature and aims to maximize share in order to get a certain profit. The model behaviours are discussed mainly from the point of view of stability, bifurcations and chaos. By utilizing Jury's stability criteria, the Cournot-Nash equilibrium's asymptotic stability is examined. We found that under certain conditions, when consumer willingness to pay was taken as a bifurcation parameter, the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation. Lyapunov exponents are used to demonstrate that the system becomes chaotic through each of the previous bifurcations.
{"title":"Nonlinear dynamic and chaos in a remanufacturing duopoly game with heterogeneous players and nonlinear inverse demand functions","authors":"Habiba Meskine, Mohammed Salah Abdelouahab, R. Lozi","doi":"10.1080/10236198.2023.2228421","DOIUrl":"https://doi.org/10.1080/10236198.2023.2228421","url":null,"abstract":"The purpose of this paper is to investigate the dynamics of a remanufacturing duopoly game model with heterogeneous players and different competition strategies, assuming that the original equipment manufacturer has bounded rationality and aims to maximize profit, and the third-party remanufacturer has an adaptive nature and aims to maximize share in order to get a certain profit. The model behaviours are discussed mainly from the point of view of stability, bifurcations and chaos. By utilizing Jury's stability criteria, the Cournot-Nash equilibrium's asymptotic stability is examined. We found that under certain conditions, when consumer willingness to pay was taken as a bifurcation parameter, the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation. Lyapunov exponents are used to demonstrate that the system becomes chaotic through each of the previous bifurcations.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75583281","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 : 2023-06-14DOI: 10.1080/10236198.2023.2222006
Narjes Khalifa, M. Benrejeb
The proposed secure communication system is based on mixed discrete-time chaotic systems in this study. To increase signal transmission security over the public channel, this system is composed of two chaotic systems on the transmitter and receiver sides. Borne and Gentina criterion associated with the Benrejeb arrow form matrix is used for stability study and system description to ensure the synchronization between these chaotic systems. The case of electrocardiogram encryption and decryption is considered an application to illustrate the effectiveness of the proposed chaotic encryption approach. The performance analyses of the proposed secure communication under the Additive White Gaussian Noise (AWGN) channel, brute force attack and some statistical attacks have shown that the proposed encryption scheme exhibited a high level of security, could maintain the confidentiality and integrity of the transmitted information and the original signal can be accurately recovered even in the presence of noise.A comparitive study between different methods is given to show the advantages and the drawbacks of the proposed communication system.
{"title":"On secure communication scheme-based mixed discrete-time hyperchaotic systems","authors":"Narjes Khalifa, M. Benrejeb","doi":"10.1080/10236198.2023.2222006","DOIUrl":"https://doi.org/10.1080/10236198.2023.2222006","url":null,"abstract":"The proposed secure communication system is based on mixed discrete-time chaotic systems in this study. To increase signal transmission security over the public channel, this system is composed of two chaotic systems on the transmitter and receiver sides. Borne and Gentina criterion associated with the Benrejeb arrow form matrix is used for stability study and system description to ensure the synchronization between these chaotic systems. The case of electrocardiogram encryption and decryption is considered an application to illustrate the effectiveness of the proposed chaotic encryption approach. The performance analyses of the proposed secure communication under the Additive White Gaussian Noise (AWGN) channel, brute force attack and some statistical attacks have shown that the proposed encryption scheme exhibited a high level of security, could maintain the confidentiality and integrity of the transmitted information and the original signal can be accurately recovered even in the presence of noise.A comparitive study between different methods is given to show the advantages and the drawbacks of the proposed communication system.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"14 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81955584","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 : 2023-06-05DOI: 10.1080/10236198.2023.2220417
E. Makhrova
ABSTRACT Let X be a dendrite and let be a continuous map that has an infinite minimal set M in X. In the article we obtain conditions on the structure of a dendrite X and the set M, under which f has an arc horseshoe, and, hence, f has a positive topological entropy. We show that this result is not correct both for continuous maps with an empty set of periodic points, and for continuous maps with a non-empty set of periodic points on finite graphs.
{"title":"Remarks on minimal sets on dendrites and finite graphs","authors":"E. Makhrova","doi":"10.1080/10236198.2023.2220417","DOIUrl":"https://doi.org/10.1080/10236198.2023.2220417","url":null,"abstract":"ABSTRACT Let X be a dendrite and let be a continuous map that has an infinite minimal set M in X. In the article we obtain conditions on the structure of a dendrite X and the set M, under which f has an arc horseshoe, and, hence, f has a positive topological entropy. We show that this result is not correct both for continuous maps with an empty set of periodic points, and for continuous maps with a non-empty set of periodic points on finite graphs.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"52 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83312183","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 : 2023-06-03DOI: 10.1080/10236198.2023.2242518
Yunping Wang, Qianhui He
In this paper, we study metric mean dimension with potential and set up a variational principle for it, which connects rate distortion function to metric mean dimension with potential. Moreover, we give alternative definitions of metric mean dimensions with potential and show that classic metric mean dimension with potential is equal to Bowen upper and lower capacity metric mean dimensions with potential.
{"title":"Variational principle for metric mean dimension with potential","authors":"Yunping Wang, Qianhui He","doi":"10.1080/10236198.2023.2242518","DOIUrl":"https://doi.org/10.1080/10236198.2023.2242518","url":null,"abstract":"In this paper, we study metric mean dimension with potential and set up a variational principle for it, which connects rate distortion function to metric mean dimension with potential. Moreover, we give alternative definitions of metric mean dimensions with potential and show that classic metric mean dimension with potential is equal to Bowen upper and lower capacity metric mean dimensions with potential.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"308 ","pages":"657 - 681"},"PeriodicalIF":1.1,"publicationDate":"2023-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72495507","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 : 2023-06-03DOI: 10.1080/10236198.2023.2242521
G. Chatzarakis, H. Péics, Andrea Rožnjik
We devoted this paper to difference equations with continuous time, having several oscillating coefficients. We established sufficient conditions that guarantee that every solution of considered equations is oscillatory. We consider difference equations of both the retarded and the advanced types. We provide several examples, illustrating the results.
{"title":"Oscillations of deviating difference equations with continuous time and oscillatory coefficients","authors":"G. Chatzarakis, H. Péics, Andrea Rožnjik","doi":"10.1080/10236198.2023.2242521","DOIUrl":"https://doi.org/10.1080/10236198.2023.2242521","url":null,"abstract":"We devoted this paper to difference equations with continuous time, having several oscillating coefficients. We established sufficient conditions that guarantee that every solution of considered equations is oscillatory. We consider difference equations of both the retarded and the advanced types. We provide several examples, illustrating the results.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"87 1","pages":"682 - 700"},"PeriodicalIF":1.1,"publicationDate":"2023-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76381789","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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