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Ramanujan-inspired series for 1/π involving harmonic numbers J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-03-09 Qing-Hu Hou, Haihong He, Xiaoxia Wang
By applying the derivative operator to the known identities from hypergeometric series or WZ pairs, we obtain six series associated with harmonic numbers. Specifically, five of them are Ramanujan-l...
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Dynamical analysis of a three-dimensional discrete-time SIR model J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-03-05 Jiangqiong Yu, Lin Li, Lingling Liu, Zhiheng Yu
In this paper, we mainly study the dynamic properties of a class of three-dimensional SIR models. First, we use the complete discriminant theory of polynomials to obtain the parameter conditions fo...
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Discrete-time models for interactive wild and transgenic sterile mosquitoes J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-03-05 Jianshe Yu, Jia Li
To gain insights into the effectiveness of the newly proposed and developed genetic sterile insect technique in control of mosquitoes, that releases mosquitoes carrying a dominant lethal (RIDL), we...
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On sensitivity and transitivity of a dynamical system and its induced dynamical systems J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-03-01 Jiandong Yin, Xiaoxiao Nie, Cheng Zhang, Chunmei Yan
Let (X,f) be a dynamical system, i.e. X is a compact metric space and f is a continuous self-map on X and let K(X), M(X) and F(X) be the sets of all non-empty compact subsets of X, Borel probabilit...
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Some limitations on the use of the basic reproduction number J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-02-23 Patrick De Leenheer, Zachary Gregg, Jordan McCaslin
We briefly review some history and some of the main mathematical properties of the basic reproduction number, a concept encountered frequently in mathematical biology. We discuss some limitations o...
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Modeling the population dynamics and movement of Zebra mussels J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-02-21 Alexanderia Lacy, Yu Jin, David Strayer, Suzanne Lenhart
Zebra mussels have caused significant damage in many lakes and rivers. By using a hybrid population model with discrete-time equations and ordinary differential equations, we represent the zebra mu...
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Recurrent sequences: key results, applications, and problems J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-02-20 Sorin Olaru
Published in Journal of Difference Equations and Applications (Ahead of Print, 2024)
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A multiplicity result in finite-dimensional vector spaces J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-02-16 Biagio Ricceri
Let f1,…,fn be n (n≥2) continuous real-valued functions on R such that lim|t|→+∞∫0tfk(s)dst2=−∞ for all k=1,…,n. This sole condition is far from ensuring the existence of multiple solutions for th...
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The new notion of Bohl dichotomy for non-autonomous difference equations and its relation to exponential dichotomy J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-02-14 Adam Czornik, Konrad Kitzing, Stefan Siegmund
In A. Czornik et al. [Spectra based on Bohl exponents and Bohl dichotomy for non-autonomous difference equations, J. Dynam. Differ. Equ. (2023)] the concept of Bohl dichotomy is introduced which is...
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Long-term averages of the stochastic logistic map J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-02-14 Maricela Cruz, Austin Wei, Johanna Hardin, Ami Radunskaya
The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions,...
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Delay-dependent set-invariance for linear difference equations with multiple delays: a polyhedral approach J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-02-14 Carlos E. T. Dórea, Sorin Olaru, Silviu-Iulian Niculescu, Vladimir Răsvan
This paper revisits the set-invariance for linear delay-difference equations and proposes novel delay-dependent notions in contrast with the existing delay-independent constructions available in th...
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Chaos theory, complexity theory, catastrophe theory, and the enigmatic concept of chaoplexity J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-02-14 René Lozi
Published in Journal of Difference Equations and Applications (Ahead of Print, 2024)
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The paths of nine mathematicians to the realm of dynamical systems J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-02-15 René Lozi, Vladimir Belykh, Jim Michael Cushing, Lyudmila Efremova, Saber Elaydi, Laura Gardini, Michał Misiurewicz, Eckehard Schöll, Galina Strelkova
This article is devoted to the first steps of nine mathematicians from five countries on their path to mathematics, chaos and discrete dynamical systems, some from early childhood. In these life st...
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Some criteria for higher order Turán inequalities in the spirit of Mařík's theorem J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-02-12 Bo Wang, Candice X. T. Zhang
By using Mařík's theorem and the theory of multiplier sequences, we give some sufficient conditions for proving the higher order Turán inequalities for nonnegative sequences. As an immediate conseq...
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General q-series transformations based on Abel's lemma on summation by parts and their applications J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-01-19 Jianan Xu, Xinrong Ma
In this paper, we establish three new and general transformations with sixteen parameters and bases via Abel's lemma on summation by parts. As applications, we set up a lot of new transformations o...
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Metric mean dimension of irregular sets for maps with shadowing J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-01-22 Magdalena Foryś-Krawiec, Piotr Oprocha
We study the metric mean dimension of Φ-irregular set IΦ(f) in dynamical systems with the shadowing property. In particular, we prove that for dynamical systems with the shadowing property containi...
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Extending nonstandard finite difference scheme rules to systems of nonlinear ODEs with constant coefficients J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-01-05 Marc E. Songolo, Brigitte Bidégaray-Fesquet
In this paper, we present a reformulation of Mickens' rules for nonstandard finite difference (NSFD) schemes to adapt them to systems of ODEs. We want to compare several methods within the class of...
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Bifurcation analysis in a discrete toxin-producing phytoplankton–zooplankton model with refuge J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-01-03 Lijuan Niu, Qiaoling Chen, Zhidong Teng
This paper concerns a discrete-time phytoplankton–zooplankton model in which the effects of toxin produced by phytoplankton and refuges provided for phytoplankton on the interactions between phytop...
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A higher order compact numerical approach for singularly perturbed parabolic problem with retarded term J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2024-01-03 Gajendra Babu, Kapil K. Sharma, Komal Bansal
In this work, a compact finite difference approach is constructed for singularly perturbed parabolic reaction diffusion problems with a retarded term. The time and space derivatives have been discr...
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Unique special solution for discrete Painlevé II J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-12-27 Walter Van Assche
We show that the discrete Painlevé II equation with starting value a−1=−1 has a unique solution for which −1
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Bifurcation, chaos and multi-stability regions in an asset pricing model with three subsystems J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-12-21 En-Guo Gu, Jun Ni, Zhao-Hui He
An asset pricing model with two types of chartists and fundamentalists and trend followers is considered, it is driven by a two-dimensional piecewise linear discontinuous map with three subsystems....
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Minimality and distributional chaos in triangular maps J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-12-21 Francisco Balibrea, Lenka Rucká
The result of this paper contributes to the classification of triangular maps of the square with zero topological entropy stated by A. N. Sharkovsky in the 1980s. The problem was if a triangular ma...
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A dynamically consistent nonstandard finite difference scheme for a generalized SEIR epidemic model J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-12-14 Manh Tuan Hoang, Matthias Ehrhardt
This work is devoted to the proposal and analysis of a new mathematical study of the transmission dynamics of infectious diseases. First, a generalized SEIR epidemic model is presented that uses ge...
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Some characterizations of the symmetric q-Dunkl-semiclassical orthogonal q-polynomials J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-12-12 H. M. Srivastava, Jihad Souissi, Mohamed Khalfallah
In this paper, we introduce a new class of symmetric orthogonal polynomials, which generalizes the q-Dunkl-classical polynomials and also provides new characterizations of symmetric q-semiclassical...
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Error analysis of a weak Galerkin finite element method for singularly perturbed differential-difference equations J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-12-08 Şuayip Toprakseven, Xia Tao, Jiaxiong Hao
A weak Galerkin finite element method is applied to singularly perturbed delay reaction-diffusion problems. A robust uniform convergence has been proved both in the energy and balanced norms using ...
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Solvability and convergence analysis of a transformed L1 finite difference scheme for TFMBE models without slope selection J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-12-05 Min Li, Boya Zhou, Menghan Zhang, Wei Gu
This paper presents a transformed L1 finite difference method for the time-fractional molecular beam epitaxy (TFMBE) model without slope selection, taking the initial singularity of the solution in...
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Monotone continuous solutions of an equation in linear combination of alternative iterates J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-29 Yeming Chen, Yingying Zeng, Weinian Zhang, Linfeng Zhou
Iteration is one of the most important topics in computer science and attentions are paid to functional equations involving iterates, one of which is the linear combination of alternative iterates....
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The impact of dispersal and allee effects on tick invasion: a spatially-explicit discrete-time modelling approach J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-12-02 Azmy S. Ackleh, Amy Veprauskas, Aijun Zhang
We develop a spatially-explicit discrete-time model that describes tick population dynamics and incorporates the developmental stages for an individual tick. The model allows for two types of movem...
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Relatively pointwise recurrence on local dendrites J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-27 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...
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Existence of the carrying simplex for a retrotone map J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-23 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...
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On the dynamics of non-Volterra quadratic operators corresponding to permutations J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-23 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 ...
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Experimenting with discrete dynamical systems J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-23 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...
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Global asymptotic stability of evolutionary periodic Ricker competition models J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-21 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...
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Controlled two-dimensional Markov chains between two absorbing barriers J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-20 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...
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On a conjectural series of Sun for the mathematical constant β(4) J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-20 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...
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Foreword to the special issue of Journal of Difference Equations and Applications on ‘Lozi, Hénon, and other chaotic attractors, theory and applications’ J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-16 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...
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A generalized family of transcendental functions with one dimensional Julia sets J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-13 Xu Zhang
A 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 e...
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Invariant curves in a discrete-time two-species system J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-09 Ryusuke Kon
The dynamics of discrete-time two-species systems may not be simple even if they have no positive fixed points. To reveal the behaviour of such systems, we focus on a special class of discrete-time...
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Wolbachia spread dynamics in mosquito populations in cyclic environments J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-09 Bo Zheng, Jianshe Yu
In 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 establish...
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Ultradiscrete hungry Toda equation and eigenvalues over min-plus algebra J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-11-03 Masafumi Kan, Akiko Fukuda, Sennosuke Watanabe
The recursion formula of the quotient difference algorithm for computing matrix eigenvalues corresponds with the discrete Toda equation, which is well-known in discrete integrable systems. Previous...
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Global dynamics results for a class of planar cooperative maps J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-17 M. R. S. Kulenović, J. Marcotte, O. Merino
Sufficient conditions are given for planar cooperative maps to have the qualitative global dynamics determined solely on local stability information obtained from fixed and minimal period-two point...
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Population growth in discrete time: a renewal equation oriented survey J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-13 B. Boldin, O. Diekmann, J. A. J. Metz
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabil...
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A new extension of a “divergent” Ramanujan-type supercongruence J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-17 Jian Cao, Victor J. W. Guo, Xiao Yu
We give a new extension of a ‘divergent’ Ramanujan-type supercongruence of Guillera and Zudilin by establishing a q-analogue of this result. Our proof makes use of the ‘creative microscoping’ metho...
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Analysis of a numerical technique for a singularly perturbed parabolic convection–diffusion interface problem with time delay J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-09 S. Chandra Sekhara Rao, Abhay Kumar Chaturvedi
In this article, we are interested in the numerical analysis of a singularly perturbed parabolic differential equation with time delay. The source term of the considered problem has discontinuities...
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n-dimensional Kolmogorov maps, carrying simplices, and bifurcations at the origin J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-13 William T. Jamieson, Orlando Merino
For a Kolmogorov map on the positive cone of Rn or an order interval determined by the origin and a positive element of Rn, sufficient conditions are given for the existence of a carrying simplex a...
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Correction Statement J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-09
Published in Journal of Difference Equations and Applications (Vol. 29, No. 8, 2023)
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Evolution of dispersal by memory and learning in integrodifference equation models J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-11 Robert Stephen Cantrell, Chris Cosner, Ying Zhou
In this paper, we develop an integrodifference equation model that incorporates spatial memory and learning so that each year, a fraction of the population use the same dispersal kernel as the prev...
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Border-collision bifurcations from stable fixed points to any number of coexisting chaotic attractors J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-09 D. J. W. Simpson
In diverse physical systems stable oscillatory solutions devolve into more complicated solutions through border-collision bifurcations. Mathematically these occur when a stable fixed point of a pie...
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Variational principles for pointwise preimage entropies J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-09 Yaling Shi, Kesong Yan, Fanping Zeng
Based 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 vi...
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Attractive sets of periodic integrodifference equations under discretization J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-04 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 ...
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A note on a functional equation model of decay processes: analysis and consequences J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-05 Ronald E. Mickens, Sandra A. Rucker
It is known that many physical systems undergoing (nuclear, atomic, etc.) decay do not obey the standard decreasing exponential formula which corresponds to the solution of a first-order, linear OD...
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Generalized Fibonacci–Leonardo numbers J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-10-04 Urszula Bednarz, Małgorzata Wołowiec-Musiał
In 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 classi...
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Capturing chaos: a multidisciplinary approach to nonlinear population dynamics J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-09-29 Robert A. Desharnais, Shandelle M. Henson, R. F. Costantino, Brian Dennis
The 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...
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On some rational piecewise linear rotations J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-09-26 Anna Cima, Armengol Gasull, Víctor Mañosa, Francesc Mañosas
We 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 t...
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Dynamics of a rational map: unbounded cycles, unbounded chaotic intervals and organizing centres J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-09-13 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...
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A unimodal sequence with mode at a quarter length J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-09-07 Max Y. C. Liu, David G. L. Wang
ABSTRACT We show that the number A(n,m)A(n,m) of partitions with m even parts and largest hook length n is strongly unimodal with mode ⌊(n−1)/4⌋⌊(n−1)/4⌋ for n≥6n≥6 . We establish this result by induction, using a 5-term recurrence due to Lin, Xiong and Yan, and two 4-term recurrences obtained by Zeilberger's algorithm. The sequence A(n,m)A(n,m) is not log-concave. Using Möbius transformation and the
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The asymptotic log-convexity of Apéry-like numbers J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-09-06 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.
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Self-reciprocal polynomials connecting unsigned and signed relative derangements J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-09-01 Ricky X. F. Chen, Yu-Chen Ruan
In this paper, we introduce polynomials (in x) of signed relative derangements that track the number of signed elements. Note that relative derangements are those without any signed elements, i.e. ...
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A weighted extension of Fibonacci numbers J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-08-30 Gaurav Bhatnagar, Archna Kumari, Michael J. Schlosser
We extend Fibonacci numbers with arbitrary weights and generalize a dozen Fibonacci identities. As a special case, we propose an elliptic extension which extends the q-Fibonacci polynomials appearing in Schur's work. The proofs of most of the identities are combinatorial, extending the proofs given by Benjamin and Quinn, and in the q-case, by Garrett. Some identities are proved by telescoping.
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Five classes of pattern avoiding inversion sequences under one roof: generating trees J. Differ. Equ. Appl. (IF 1.1) Pub Date : 2023-08-30 Toufik Mansour
An inversion sequence of length n is a word e=e0…en which satisfies for each i∈[n]={0,1,…,n} the inequalities 0≤ei≤i. 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