Impact of a block structure on the Lotka-Volterra model by Clenet, Maxime, Massol, François, Najim, Jamal

“…The model consists of n coupled differential equations linking the abundances of n different species. …”
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Nonlinear iterative approximation of steady incompressible chemically reacting flows by Gazca-Orozco, Pablo Alexei, Heid, Pascal, Süli, Endre

“…We consider a system of nonlinear partial differential equations modelling steady flow of an incompressible chemically reacting non-Newtonian fluid, whose viscosity depends on both the shear-rate and the concentration; in particular, the viscosity is of power-law type, with a power-law index that depends on the concentration. …”
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An efficient technique to study of time fractional Whitham–Broer–Kaup equations by Nishant Bhatnagar, Kanak Modi, Lokesh Kumar Yadav, Ravi Shanker Dubey

“…The method’s novelty and straightforward implementation establish it as a reliable and efficient analytical technique for solving both linear and nonlinear fractional partial differential equations.…”
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Analytical Solutions of Fractional Walter’s B Fluid with Applications by Qasem Al-Mdallal, Kashif Ali Abro, Ilyas Khan

“…By employing the dimensional analysis, the dimensional governing partial differential equations have been transformed into dimensionless form. …”
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Bat population dynamics: multilevel model based on individuals' energetics by Paula Federico, Dobromir T. Dimitrov, Gary F. McCracken

“…A structured population model based on extended McKendrick-von Foerster partial differential equations integrates those individual dynamics and provides insight into possible regulatory mechanisms of population size as well as conditions of population survival and extinction. …”
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Super class of implicit extended backward differentiation formulae for the numerical integration of stiff initial value problems by Hamisu Musa, Buhari Alhassan

“…An implicit Superclass of non-block Extended Backward Differentiation Formulae (SEBDF) for the numerical integration of first-order stiff system of Ordinary Differential Equations (ODEs) in Initial Value Problems (IVPs) with optimal stability properties is presented. …”
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On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions by Haobin Liu, Hassan Khan, Rasool Shah, A. A. Alderremy, Shaban Aly, Dumitru Baleanu

“…The suggested procedure is very attractive and straight forward and therefore can be modified to solve high nonlinear fractional partial differential equations and their systems.…”
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A Probabilistic Analysis to Quantify the Effect of March 11, 2004, Attacks in Madrid on the March 14 Elections in Spain: A Dynamic Modelling Approach by Juan-Carlos Cortés, Francisco Sánchez, Francisco-José Santonja, Rafael-Jacinto Villanueva

“…In this paper, we present a dynamic model based on a system of differential equations such that it, using data from Spanish CIS (National Center of Sociological Research), describes the evolution of voting intention of the Spanish people over time. …”
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ON THE TECHNIQUE OF MODELING ONTOGENETIC CHANGES IN FISH AND INSECTS LIFECYCLE by A. Yu. Perevaryukha

“…The method has been for submission to decline of generations on the basis of dynamic overriding differential equations with discrete-continuous structure of time. …”
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From the Guest Editors by Carlos Castillo-Chávez, Christopher Kribs Zaleta, Yang Kuang, Baojun Song

“…Those of us who met the field of mathematical biology as a well-developed,flourishing, and rewarding discipline owe much to those who made it so.This special issue of Mathematical Biosciences and Engineering isdedicated to two such pioneers: Fred Brauer and Karl Hadeler.Since retrospectives of both men have been published in other venues [1, 2], we will only summarize their contributions briefly here.Fred Brauer obtained his Ph.D. from MIT in 1956 under Norman Levinson,and during a long tenure at the University of Wisconsin he co-wrote severaltexts on ordinary differential equations that have become classics.His research entered mathematical biology first through early studies inpredator-prey systems and harvesting, both with and without delays.He then moved into mathematical epidemiology, and the text he co-authoredwith Carlos Castillo-Chavez in both these areas earlier this decade isalready in wide use.For more information please click the “Full Text” above.…”
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A Nonoscillatory Second-Order Time-Stepping Procedure for Reaction-Diffusion Equations by Philku Lee, George V. Popescu, Seongjai Kim

“…After a theory of morphogenesis in chemical cells was introduced in the 1950s, much attention had been devoted to the numerical solution of reaction-diffusion (RD) partial differential equations (PDEs). The Crank–Nicolson (CN) method has been a common second-order time-stepping procedure. …”
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Optical soliton solutions of the M-fractional paraxial wave equation by Md. Habibul Bashar, Md. Abde Mannaf, M. M. Rahman, Mst. Tania Khatun

“…The strategy introduced is fundamental and robust as a smart soliton solution for nonlinear partial differential equations, and it may play a crucial role in nonlinear optics, fiber optics, and communication systems.…”
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EVOLUTION OF THE ROTATIONAL MOTION OF A SATELLITE WITH FLEXIBLE VISCOELASTIC RODS ON THE ELLIPTIC ORBIT by E. V. Sadovnikova, A. V. Shatina

“…We obtain an averaged system of differential equations in the Andoyer variables, which describes the evolution of the satellite's rotational motion. …”
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Analysis of Model Parameters for a Polymer Filtration Simulator by N. Brackett-Rozinsky, S. Mondal, K. R. Fowler, E. W. Jenkins

“…The simulator is a three-dimensional, time-dependent discretization of a coupled system of nonlinear partial differential equations used to model fluid flow and debris transport, along with statistical relationships that define debris distributions and retention probabilities. …”
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Synchronization of Two Self-Synchronous Vibrating Machines on an Isolation Frame by Chunyu Zhao, Qinghua Zhao, Zhaomin Gong, Bangchun Wen

“…Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the disturbance parameters for the angular velocities of the four unbalanced rotors. …”
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Synchronous Stability of Four Homodromy Vibrators in a Vibrating System with Double Resonant Types by Xueliang Zhang, Chao Li, Zhihui Wang, Shiju Cui

“…This paper aims at studying the synchronous stability of four homodromy vibrators in subresonant and superresonant states. The motion differential equations are established firstly. The simplified form of analytical expressions is yielded, and the stability criterion of synchronous states satisfies Routh–Hurwitz criterion. …”
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A Direct Eulerian GRP Scheme for the Prediction of Gas-Liquid Two-Phase Flow in HTHP Transient Wells by Jiuping Xu, Min Luo, Jiancheng Hu, Shize Wang, Bin Qi, Zhiguo Qiao

“…A coupled system model of partial differential equations is presented in this paper, which concerns the variation of the pressure and temperature, velocity, and density at different times and depths in high temperature-high pressure (HTHP) gas-liquid two-phase flow wells. …”
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Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs by Youness El Ansari, Ali El Myr, Lahcen Omari

“…Furthermore, we use the Itô formula and some other theoretical theorems of stochastic differential equation to discuss the extinction and the stationary distribution of our system. …”
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Dubovsky’s Class of Mathematical Models for Describing Economic Cycles with Heredity Effects by Danil Makarov, Roman Parovik, Zafar Rakhmonov

“…Dubovsky, consisting of two nonlinear differential equations of fractional order and describing the dynamics of the efficiency of new technologies and the efficiency of capital productivity, taking into account constant and variable heredity. …”
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A Novel Neural Network-Based Approach Comparable to High-Precision Finite Difference Methods by Fanghua Pei, Fujun Cao, Yongbin Ge

“…Deep learning methods using neural networks for solving partial differential equations (PDEs) have emerged as a new paradigm. …”
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