Some recent developments on linear determinacy by Carlos Castillo-Chavez, Bingtuan Li, Haiyan Wang

Subjects: “…nonlinear reaction diffusion difference equations.…”
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Optimal harvesting policy for the Beverton--Holt model by Martin Bohner, Sabrina Streipert

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On the Behavior of a System of Rational Difference Equations xn+1=xn-1/(ynxn-1-1),yn+1 = yn-1/(xnyn-1-1),zn+1=1/xnzn-1 by Liu Keying, Wei Zhiqiang, Li Peng, Zhong Weizhou

“…We are concerned with a three-dimensional system of rational difference equations with nonzero initial values. We present solutions of the system in an explicit way and obtain the asymptotical behavior of solutions.…”
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On approximation of the solutions of delay differential equations by using piecewise constant arguments by Istevan Györi

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On the Behavior of Solutions of the System of Rational Difference Equations: 𝑥𝑛+1=𝑥𝑛−1/(𝑦𝑛𝑥𝑛−1−1), 𝑦𝑛+1=𝑦𝑛−1/(𝑥𝑛𝑦𝑛−1−1), and 𝑧𝑛+1=𝑧𝑛−1/(𝑦𝑛𝑧𝑛−1−1) by Abdullah Selçuk Kurbanli

“…We investigate the solutions of the system of difference equations 𝑥𝑛+1=𝑥𝑛−1/(𝑦𝑛𝑥𝑛−1−1), 𝑦𝑛+1=𝑦𝑛−1/(𝑥𝑛𝑦𝑛−1−1), 𝑧𝑛+1=𝑧𝑛−1/(𝑦𝑛𝑧𝑛−1−1), where 𝑦0,𝑦−1,𝑥0,𝑥−1,𝑧−1,𝑧0∈ℝ.…”
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3D Chaotic Nonlinear Dynamic Population-Growing Mathematical System Modeling with Multiple Controllers by Shaymaa Hussain, Suzan Obaıys, Nadia Al-saidi, Yeliz Karaca

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Models for information propagation on graphs by Oliver R. A. Dunbar, Charles M. Elliott, Lisa Maria Kreusser

Subjects: “…numerical methods for difference equations…”
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New Method of Solving the Economic Complex Systems by Ya-Juan Yang, Chung-Cheng Chen, Yen-Ting Chen

“…The economic model generally applies the discrete recurrence difference equation. The significant analytic approach for the difference equation is the z-transformation technique. …”
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On Dynamical Behavior of Discrete Time Fuzzy Logistic Equation by Qianhong Zhang, Fubiao Lin

“…The aim of this paper is to investigate the dynamical behavior of the following model which describes the logistic difference equation taking into account the subjectivity in the state variables and in the parameters. xn+1=Axn(1~-xn),  n=0,1,2,⋯, where {xn} is a sequence of positive fuzzy numbers. …”
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Research on Roll Stabilizing Based on Energy Optimization for Autonomous Surface Vehicle by Hongjian Wang, Linlin Wang, Lixin Pan

“…Coupling horizontal motion model of ASV is decoupled, and an equivalent transfer function of roll motion is obtained and transformed into a discrete difference equation through inverse Laplace transformation and Euler approximation. …”
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Oscillation Criteria for Second-Order Delay, Difference, and Functional Equations by L. K. Kikina, I. P. Stavroulakis

“…The most interesting oscillation criteria for the second-order linear delay differential equation, the second-order difference equation and the second-order functional equation, especially in the case where liminft→∞∫τ(t)tτ(s)p(s)ds≤1/e and limsupt→∞∫τ(t)tτ(s)p(s)ds<1 for the second-order linear delay differential equation, and 0<liminft→∞{Q(t)P(g(t))}≤1/4 and limsupt→∞{Q(t)P(g(t))}<1, for the second-order functional equation, are presented.…”
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The general solutions of difference vector-equations with constant coefficients by Artūras Štikonas

“…We find the simple formulae between solution of the first order homogeneous differential equations and solution of difference equation. This allows easily get all solutions of difference equations if we know the differential solution. …”
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On the recursive sequence xn+1=−1/xn+A/xn−1 by Stevo Stević

“…We investigate the periodic character of solutions of the nonlinear difference equation xn+1=−1/xn+A/xn−1. We give sufficient conditions under which every positive solution of this equation converges to a period two solution. …”
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Permanence and Global Attractivity of Discrete Predator-Prey System with Hassell-Varley Type Functional Response by Runxin Wu, Lin Li

“…By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator-prey system with Hassell-Varley type functional response are obtained. …”
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Permanence of a Discrete Predator-Prey Systems with Beddington-DeAngelis Functional Response and Feedback Controls by Xuepeng Li, Wensheng Yang

“…By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system.…”
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Uniqueness and Multiplicity of Solutions for a Second-Order Discrete Boundary Value Problem with a Parameter by Xi-Lan Liu, Jian-Hua Wu

“…This paper is concerned with the existence of unique and multiple solutions to the boundary value problem of a second-order difference equation with a parameter, which is a complement of the work by J. …”
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Some New Discrete Gronwall-Bellman Type Inequalities with Three Independent Variables and Applications by Weihua Liu, Haisong Huang

“…Some new discrete Gronwall-Bellman type inequalities with three independent variables which generalize some existing results and can be used as handy tools in the study of qualitative and quantitative properties of solutions of certain classes of difference equation are presented. As applications, some difference equations with the initial boundary conditions are also considered.…”
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Existence of Solutions for the Discrete Dirichlet Problem Involving p-Mean Curvature Operator by Jianxia Wang, Zhan Zhou

“…This work is to discuss the Dirichlet boundary value problem of the difference equation with p -mean curvature operator. Under some determinate growth conditions on the nonlinear term, the existence of one solution or two nontrivial solutions is obtained via variational methods and some analysis techniques. …”
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A Note on Stability of an Operator Linear Equation of the Second Order by Janusz Brzdȩk, Soon-Mo Jung

“…We prove some Hyers-Ulam stability results for an operator linear equation of the second order that is patterned on the difference equation, which defines the Lucas sequences (and in particular the Fibonacci numbers). …”
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Permanence and Global Attractivity of the Discrete Predator-Prey System with Hassell-Varley-Holling III Type Functional Response by Runxin Wu, Lin Li

“…By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator-prey system with Hassell-Varley-Holling III type functional response are obtained. …”
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