Dynamics of an ultra-discrete SIR epidemic model with time delay by Masaki Sekiguchi, Emiko Ishiwata, Yukihiko Nakata

“…It is proven that the ultra-discrete model has a threshold property concerning global attractivity of equilibria as shown in differential and difference equation models. We also study an interesting convergence pattern of the solution, which is illustrated in a two-dimensional lattice.…”
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Comparison of the Wiener and Kirchhoff Indices of Random Pentachains by Shouliu Wei, Wai Chee Shiu, Xiaoling Ke, Jianwu Huang

“…In this paper, explicit formulae for the expected values of the Wiener and Kirchhoff indices of random pentachains are derived by the difference equation and recursive method. Based on these formulae, we then make comparisons between the expected values of the Wiener index and the Kirchhoff index in random pentachains and present the average values of the Wiener and Kirchhoff indices with respect to the set of all random pentachains with n pentagons.…”
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On the Recursive Sequence 𝑥𝑛+𝟏=max{𝑥𝑛,𝐴}/𝑥𝟐𝑛𝑥𝑛−𝟏 by Ibrahim Yalcinkaya, Cengiz Cinar, Ali Gelisken

“…We investigate the periodic nature of the solution of the max-type difference equation 𝑥𝑛+1=max{𝑥𝑛,𝐴}/𝑥2𝑛𝑥𝑛−1, 𝑛=0,1,2,…, where the initial conditions are 𝑥−1=𝐴𝑟1 and 𝑥0=𝐴𝑟2 for 𝐴∈(0,∞), and that 𝑟1 and 𝑟2 are positive rational numbers. …”
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Functions Induced by Iterated Deformed Laguerre Derivative: Analytical and Operational Approach by Sladjana D. Marinković, Miomir S. Stanković, Predrag M. Rajković

“…We study their properties, such as representation, orthogonality, generating function, differential and difference equation, and addition and summation formulas. …”
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Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales by Shuhong Tang, Tongxing Li, Ethiraju Thandapani

“…Our results not only improve and complement those results in the literature but also unify the oscillation of the second-order half-linear advanced differential equation and the second-order half-linear advanced difference equation. Three examples are included to illustrate the main results.…”
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Problems for combinatorial numbers satisfying a class of triangular arrays by Igoris Belovas

“… Numbers satisfying a class of triangular arrays, defined by a bivariate first-order linear difference equation with linear coefficients, include a wide range of combinatorial numbers: binomial coefficients, Morgan numbers, Stirling numbers of the first and the second types, non-central Stirling numbers, Eulerian numbers, Lah numbers, and their generalizations. …”
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On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i) by E. M. E. Zayed, M. A. El-Moneam

“…The main objective of this paper is to study the boundedness character, the periodic character, the convergence, and the global stability of the positive solutions of the difference equation xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i), n=0,1,2,…, where A, B, αi, βi and the initial conditions x−k,...…”
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A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method by Qiaojie Li, Zhoushun Zheng, Shuang Wang, Jiankang Liu

“…The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. …”
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Hyers–Ulam Stability for Quantum Equations of Euler Type by Douglas R. Anderson, Masakazu Onitsuka

“…Many applications using discrete dynamics employ either q-difference equations or h-difference equations. In this work, we introduce and study the Hyers–Ulam stability (HUS) of a quantum (q-difference) equation of Euler type. …”
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Traffic Behavior in CA Model of Vehicular Traffic through a Series of Signals by Kazuhiro Tobita, Takashi Nagatani

“…The CA model is not described by a set of rules but is given by a difference equation. The vehicular traffic varies highly with both signal’s characteristics and vehicular density. …”
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Almost Periodic Solution of a Multispecies Discrete Mutualism System with Feedback Controls by Hui Zhang, Feng Feng, Bin Jing, Yingqi Li

“…We firstly obtain the permanence of the system by utilizing the theory of difference equation. By means of constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique positive almost periodic solution which is uniformly asymptotically stable. …”
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Basin of Attraction through Invariant Curves and Dominant Functions by Ziyad AlSharawi, Asma Al-Ghassani, A. M. Amleh

“…We study a second-order difference equation of the form zn+1=znF(zn-1)+h, where both F(z) and zF(z) are decreasing. …”
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On the Recursive Sequence xn=1+∑i=1kαixn−pi/∑j=1mβjxn−qj by Stevo Stevic

“…We give a complete picture regarding the behavior of positive solutions of the following important difference equation: xn=1+∑i=1kαixn−pi/∑j=1mβjxn−qj, n∈ℕ0, where αi, i∈{1,…,k}, and βj, j∈{1,…,m}, are positive numbers such that ∑i=1kαi=∑j=1mβj=1, and pi, i∈{1,…,k}, and qj, j∈{1,…,m}, are natural numbers such that p1<p2<⋯<pk and q1<q2<⋯<qm. …”
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Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales by H. A. Agwa, Ahmed M. M. Khodier, Heba A. Hassan

“…Also, our results unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping. Finally, we give some examples to illustrate our main results.…”
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A Model for Service Life Control of Selected Device Systems by Zieja Mariusz, Ważny Mariusz

“…For estimation of deviation increasing rate in probabilistic sense, was used a difference equation from which, after transformation, Fokker-Planck differential equation was obtained [4, 11]. …”
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Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations by Răzvan O. Moşincat, Ciprian Preda, Petre Preda

“…Roughly speaking, we prove that if the solution of the corresponding inhomogeneous difference equation belongs to any sequence space (on which the right shift is an isometry) for every inhomogeneity from the same class of sequence spaces, then the continuous-time solutions of the autonomous homogeneous differential equation will exhibit a (no past) exponential dichotomic behavior. …”
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Thermal Property of Granite in Deep Strata and Its Effect on Thermal Zone of Surrounding Rock by Peng Xiang, Hui-Ci Xu, Hong-Guang Ji, Qi Li, Huan Wang

“…According to the difference equation based on the principle of heat balance, the numerical solution of unsteady heat conduction of surrounding rock can be deduced. …”
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Modeling Dominant Height Growth in Planted Pinus pinea Stands in Northwest of Tunisia by Sghaier Tahar, Palahi Marc, Garchi Salah, Bonet José Antonio, Ammari Youssef, Pique Miriam

“…Six generalized algebraic difference equations (GADAs) derived from the base models of log-logistic, Bertalanffy-Richards, and Lundqvist-Korf were used to develop site index model for Pinus pinea plantations in north-west of Tunisia. …”
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Estimates for the norms of solutions of delay difference systems by Rigoberto Medina

“…Applications to partial difference equations, which model diffusion and reaction processes, are given.…”
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A New Part-Metric-Related Inequality Chain and an Application by Xiaofan Yang, Fangkuan Sun, Yuan Yan Tang

“…Part-metric-related (PMR) inequality chains are elegant and are useful in the study of difference equations. In this paper, we establish a new PMR inequality chain, which is then applied to show the global asymptotic stability of a class of rational difference equations.…”
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