Dynamic Behaviors and Analytical Solutions of the Damped (2+1)-Dimensional Nonlinear Schrödinger Equation by Yongyi Gu, Feng Ye, Baixin Chen, Najva Aminakbari

“…Our results indicate that the extended systematic method for solving differential equations is more convenient and yields richer solutions. …”
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Peridynamic Formulation for Coupled Thermoelectric Phenomena by Migbar Assefa, Xin Lai, Lisheng Liu, Yang Liao

“…This is because traditional methods are developed based on partial differential equations (PDEs) and lead to infinite fluxes at the discontinuities. …”
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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 first one is a continuous SEIR model described by a system of ordinary differential equations. 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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Modeling the Effects of Nonpharmaceutical Interventions on COVID-19 Spread in Kenya by Duncan K. Gathungu, Viona N. Ojiambo, Mark E. M. Kimathi, Samuel M. Mwalili

“…The resulting system of ordinary differential equations (ODEs) is solved using fourth-order and fifth-order Runge–Kutta methods. …”
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A Simple Mathematical Model of Cyclic Circadian Learning by J. Šimon, M. Bulko

“…By the use of these functions and by formalism of differential equations, the concurrent processes of learning and forgetting are described mathematically. …”
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Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics by Mei Yan, Yongfeng Li, Zhongyi Xiang

“…In order to better control the pests, two-time delayed stage-structured predator-prey models with birth pulse and pest control tactics are proposed and analyzed by using impulsive differential equations in present work. The stability threshold conditions for the mature prey-eradication periodic solutions of two models are derived, respectively. …”
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Investigation of Subcombination Internal Resonances in Cantilever Beams by Haider N. Arafat, Ali H. Nayfeh

“…The method of time-averaged Lagrangian and virtual work is used to determine six nonlinear ordinary-differential equations governing the amplitudes and phases of the three interacting modes. …”
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Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach by Yonggui Kao, Hamid Reza Karimi

“…By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations (SODE) and using Itô formula, we establish some novel stability principles for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, and exponential stability in mean of partial variables for CSRDSNs. …”
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Competition and Dispersal Delays in Patchy Environments by Nancy Azer, P. van den Driessche

“…The model is formulated as a system of integro-differential equations with an arbitrary distribution of dispersal times between patches. …”
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Vibration Characteristics for Moving Printing Membrane with Variable Density along the Lateral Direction by Mingyue Shao, Jimei Wu, Yan Wang, Qiumin Wu, Yuan Chen

“…The transverse vibration differential equations of moving membrane are established based on D’Alembert’s principle and discretized by using the differential quadrature method (DQM). …”
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Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet by Meysam Mohamadali, Nariman Ashrafi

“…Upon proper scaling and by means of an exact similarity transformation, the nonlinear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Numerical solutions to the resulting boundary value problem are obtained using an efficient shooting technique in conjunction with a variable stepping method for different values of pressure gradients. …”
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On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells by Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel

“…The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. …”
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Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays by Fulgensia Kamugisha Mbabazi, Joseph Y. T. Mugisha, Mark Kimathi

“…The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratio R0 is less than unity and unstable otherwise. …”
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Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model by Fabien Crauste

“…We analyze the asymptotic stability of a nonlinear system of two differential equations with delay,describing the dynamics of blood cell production. …”
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Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument by Kuo-Shou Chiu

“…Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. …”
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Solving arbitrary one-loop reduction via generating function by Tingfei Li, Yuekai Song, Liang Zhang

“…We first establish the partial differential equations governing the higher-pole generating function. …”
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Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method by E. H. Doha, W. M. Abd-Elhameed

“…The proposed algorithms are extended to solve the two-dimensional sixth-order differential equations. A family of symmetric generalized Jacobi polynomials is introduced and used as basic functions. …”
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Analysis of SI models with multiple interacting populations using subpopulations by Evelyn K. Thomas, Katharine F. Gurski, Kathleen A. Hoffman

“…Computing endemic equilibria and basic reproductive numbers for systems of differential equations describing epidemiological systems with multiple connections between subpopulations is often algebraically intractable. …”
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The Quantum Analysis of Nonlinear Optical Parametric Processes with Thermal Reservoirs by Tamirat Abebe, Nebiyu Gemechu, Chimdessa Gashu, Kebede Shogile, Solomon Hailemariam, Shimelis Adisu

“…In this paper, employing the stochastic differential equations associated with the normal ordering, the quantum properties of a nondegenerate three-level cascade laser with a parametric amplifier and coupled to a two-mode thermal reservoir are thoroughly analyzed. …”
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Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes by Xiongwei Liu, Junjun Xu, Xiao Wang, Lizhi Cheng

“…This paper investigates two methods of releasing transgenic mosquitoes and proposes two epidemic models involving malaria patients, anopheles, wild mosquitoes, and transgenic mosquitoes based on system of continuous differential equations. A basic reproduction number R0 is defined for the models and it serves as a threshold parameter that predicts whether malaria will spread. …”
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