Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity by Wencai Zhao, Juan Li, Xinzhu Meng

“…Firstly, by using stroboscopic map and fixed point theory of difference equations, the existence of disease-free periodic solution is discussed, and the globally asymptotical stability of disease-free periodic solution is proven by using Floquet multiplier theory and differential impulsive comparison theorem. …”
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Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method by Josef Diblík

“…The paper investigates the exponential stability of a linear system of difference equations with variable delays xk+1=Axk+∑i=1sBikxk-mik, k=0,1,… , where s∈N, A is a constant square matrix, Bik are square matrices, mik∈N∪0, and mik≤m for an m∈N. …”
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Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications by F. Toutounian, Emran Tohidi, A. Kilicman

“…This paper introduces Fourier operational matrices of differentiation and transmission for solving high-order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for generalized Pantograph equations with variable coefficients by using Legendre Gauss collocation nodes. …”
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H∞ Estimation for a Class of Lipschitz Nonlinear Discrete-Time Systems with Time Delay by Huihong Zhao, Chenghui Zhang, Guangchen Wang, Guojing Xing

“…Finally, through guaranteeing the positivity of the minimum, a sufficient condition for the existence of the H∞ estimator is proposed and the estimator is derived in terms of Riccati-like difference equations. The proposed algorithm is proved to be effective by a numerical example.…”
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From Fibonacci Sequence to the Golden Ratio by Alberto Fiorenza, Giovanni Vincenzi

“…We consider the well-known characterization of the Golden ratio as limit of the ratio of consecutive terms of the Fibonacci sequence, and we give an explanation of this property in the framework of the Difference Equations Theory. We show that the Golden ratio coincides with this limit not because it is the root with maximum modulus and multiplicity of the characteristic polynomial, but, from a more general point of view, because it is the root with maximum modulus and multiplicity of a restricted set of roots, which in this special case coincides with the two roots of the characteristic polynomial. …”
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Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting by Karima Mokni, Mohamed Ch-Chaoui

“…The model is formulated in terms of difference equations and derived by using the higher-order implicit Runge Kutta method with a very small step size to attain a discrete time version of its continuous counterpart. …”
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Kannan Contraction Maps on the Space of Null Variable Exponent Second-Order Quantum Backward Difference Sequences of Fuzzy Functions and Its Pre-Quasi Ideal by Awad A. Bakery, OM Kalthum S. K. Mohamed

“…There are also some significant applications of the existence of solutions to nonlinear difference equations of fuzzy functions.…”
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Outer Synchronization of Complex Networks with Nondelayed and Time-Varying Delayed Couplings via Pinning Control or Impulsive Control by Jianwen Feng, Sa Sheng, Ze Tang, Yi Zhao

“…Based on the generalized inequality about time-varying delayed different equation, the sufficient conditions for outer synchronization are derived. …”
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Hierarchical band gaps in complex periodic systems by Dunckley, Lucas, Davies, Bryn

“…We study a class of difference equations with periodic coefficients and show that they inherit spectral gaps from their constituent elements. …”
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Stepwise fuzzy correction of the algorithm filters of random signals by A. A. Lobaty, A. S. Radkevich

“…It is assumed that the gauges are discrete and are described, like the original process assessed, by a discrete mathematical model in the form of difference equations. As an estimation algorithm, we consider a discrete Kalman filter, which, in the general case, when mathematical models are inadequate to real processes, can give distorted information. …”
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Prediction of influenza peaks in Russian cities: Comparing the accuracy of two SEIR models by Vasiliy N. Leonenko, Sergey V. Ivanov

“…The second one is a discrete model formulated as a set of difference equations, which was used in the Baroyan-Rvachev modeling framework for the influenza outbreak prediction in the Soviet Union. …”
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Stability Analysis of the Bat Algorithm Described as a Stochastic Discrete-Time State-Space System by Janusz Piotr Paplinski

“…The equations describing the bat algorithm have the form of difference equations, and the algorithm can be treated as a stochastic discrete-time system. …”
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Permanence for a Generalized Discrete Neural Network System by Stevo Stevic

“…We prove that the system of difference equations xn+1(i)=λixn(i)+fi(αixn(i+1)−βixn−1(i+1)), i∈{1,2,…,k}, n∈ℕ, (we regard that xn(k+1)=xn(1)) is permanent, provided that αi≥βi, λi+1∈[0,βi/αi), i∈{1,2,…,k}, fi:ℝ→ℝ, i∈{1,2,…,k}, are nondecreasing functions bounded from below and such that there are δi∈(0,1) and M>0 such that fi(αix)≤δix, i∈{1,2,…,k}, for all x≥M. …”
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The role of multiple modeling perspectives in students' learning of exponential growth by Carlos Castillo-Garsow

“…The exponential is among the most important family functions in mathematics; the foundation for the solution of linear differential equations, linear difference equations, and stochastic processes. However there is little research and superficial agreement on how the concepts of exponential growth are learned and/or should be taught initially. …”
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Discrete Models of Disease and Competition by R. Bravo de la Parra, M. Marvá, E. Sánchez, L. Sanz

“…We carry out a complete mathematical analysis of the asymptotic behavior of the solutions of the corresponding systems of difference equations and derive interesting ecological information about the influence of a disease in competition dynamics. …”
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Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect by A. Brett, M. R. S. Kulenović

“…We consider the following system of difference equations: xn+1=xn2/B1xn2+C1yn2, yn+1=yn2/A2+B2xn2+C2yn2,  n=0, 1, …,   where B1, C1, A2, B2, C2 are positive constants and x0, y0≥0 are initial conditions. …”
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Adaptive control of single-input single-output hybrid systems possessing interacting discrete- and continuous-time dynamics by M. de la Sen

“…As a result there are also mixed continuous-time and discrete signals present in the system associated either with the solutions of differential equations which depend at the same time on both discrete-time and continuous-time forcing terms and on generalized difference equations associated with discretized and digital signals. …”
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Mathematical Modeling of the Propagation of Democratic Support of Extreme Ideologies in Spain: Causes, Effects, and Recommendations for Its Stop by E. De la Poza, L. Jódar, A. Pricop

“…By considering the dynamic subpopulations transits built throughout data obtained from public and private prestigious institutions and sociopolitical analysis, a system of difference equations models the electoral population behavior in Spain allowing us to compute the expected electoral support in the time horizon of January 2016. …”
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Development of a Solar-Powered Incubator for Poultry Eggs by Joseph Abutu, Mainigi Umar, James Wamayi Midala, Abdulkarim Muhammad Odeh, Garkuwa Haruna, Christian Ike, Sunday Albert Lawal

“…The design of the incubator was carried out using the different equations stipulated in literatures. Also, the performance of the incubator was investigated by determining the system temperature, relative humidity, percentage fertility and hatchability. …”
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Development of a Solar-Powered Incubator for Poultry Eggs by Joseph Abutu, Mainigi Umar, James Wamayi Midala, Abdulkarim Muhammad Odeh, Garkuwa Haruna, Christian Ike, Sunday Albert Lawal

“…The design of the incubator was carried out using the different equations stipulated in literatures. Also, the performance of the incubator was investigated by determining the system temperature, relative humidity, percentage fertility and hatchability. …”
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