Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption by Xiaofeng Li, Yulong Bai, Weishuan Pan, Di Wang, Yong-Jie Ma

“…Fourth-order autonomous nonlinear differential equations can exhibit chaotic properties. In this study, we propose a family of fourth-order chaotic systems with infinite equilibrium points whose equilibria form closed curves of different shapes. …”
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Study of the Radical Chain Mechanism of Hydrocarbon Oxidation for In Situ Combustion Process by Alexandra Ushakova, Vladislav Zatsepin, Mikhail Varfolomeev, Dmitry Emelyanov

“…The system of differential equations based on the equations of oxidation reactions was solved. …”
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Exploring the implications of ternary Jeffrey nanofluid on pulsating flow and heat transfer through unsymmetrical corrugated micro conduit by Mohamed S. Abdel-wahed, Khaled S. Mekheimer, Ahmed Y. Sayed, Shaaban I. Ahmed

“…Using the perturbation method and Mathematica software, we derived semi-analytical solutions for the governing partial differential equations in their complex form. nanoparticle-enhanced blood exhibits improved thermal performance compared to pure fluid, with the type and concentration of nanoparticles (Fe3O4, Au, SWCNTs) significantly impacting heat dissipation and temperature distribution within the microfluidic conduit. …”
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Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics by Karen R. Ríos-Soto, Baojun Song, Carlos Castillo-Chavez

“…A metapopulation framework based on a system of nonlinear ordinary differential equations is used to study the transmission dynamics and control of avian diseases. …”
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The analysis of the influence of the turbulence model selection on the parameters of interaction of a supersonic jet with an obstacle by R. A. Peshkov, A. S. Shmetkova, O. V. Ispravnikova, Ju. L. Suskina

“…The study analyzes the case of interaction of a single supersonic gas jet with a flat barrier oriented perpendicular to the direction of the jet. Differential equations describing the motion of a compressible viscous heatconducting gas (Navier-Stokes equations) are presented, and a method for averaging them by Reynolds is described. …”
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Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen by Gregory Zitelli, Seddik M. Djouadi, Judy D. Day

“…The inflammatory responseaims to restore homeostasis by means of removing a biological stress, such as an invading bacterial pathogen.In cases of acute systemic inflammation, the possibility of collateral tissuedamage arises, which leads to a necessary down-regulation of the response.A reduced ordinary differential equations (ODE) model of acute inflammation was presented and investigated in [10]. …”
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Application of physics-informed neural networks (PINNs) solution to coupled thermal and hydraulic processes in silty sands by Yuan Feng, Jongwan Eun, Seunghee Kim, Yong-Rak Kim

“…Recently, physics-informed neural networks (PINNs), which incorporate partial differential equations (PDEs) to solve forward and inverse problems, have attracted increasing attention in machine learning research. …”
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Investigation of Micro- and Nanosized Particle Erosion in a 90° Pipe Bend Using a Two-Phase Discrete Phase Model by M. R. Safaei, O. Mahian, F. Garoosi, K. Hooman, A. Karimipour, S. N. Kazi, S. Gharehkhani

“…The 3-D governing differential equations were discretized using finite volume method. …”
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Robust pareto multiobjective optimum design of FG-Beam under moving mass by Moein Abdollah-Salimi, Nader Nariman-Zadeh, Reza Ansari

“…By substituting terms of energy into the Lagrange equation, differential equations of motion are obtained. Displacement fields as a function of time and x-coordinate are calculated by means of the numerical solution of the above-mentioned equations. …”
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Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents by Raimund BÜrger, Gerardo Chowell, Elvis GavilÁn, Pep Mulet, Luis M. Villada

“…An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. …”
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Modeling bacterial attachment to surfaces as an early stage of biofilm development by Fadoua El Moustaid, Amina Eladdadi, Lafras Uys

“…While much is known about the later stages of biofilm formation, less is known about its initiation which is an important first step in the biofilm formation.In this paper, we develop a non-linear system of partial differential equations of Keller-Segel type model in one-dimensional space, which couples the dynamics of bacterial movement to that of the sensing molecules. …”
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Solutions of Cauchy Problems for the Caudrey–Dodd–Gibbon–Kotera–Sawada Equation in Three Spatial and Two Temporal Dimensions by Yufeng Zhang, Linlin Gui

“…Fokas has obtained integrable nonlinear partial differential equations (PDEs) in 4 + 2 dimensions by complexifying the independent variables. …”
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Explicit scheme based on integral transforms for estimation of source terms in diffusion problems in heterogeneous media by André José Pereira de Oliveira, Luiz Alberto da Silva Abreu, Diego Campos Knupp

“… The estimation of source terms present in differential equations has various applications, ranging from structural assessment, industrial process monitoring, equipment failure detection, environmental pollution source detection to identification applications in medicine. …”
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Influence of different delays on mixed types of oscillations under limited excitation by A. A. Alifov

“…With the account of the interaction with the energy source, the known calculation scheme (or model) of a mechanical frictional self-oscillating system serves as a unified basis for considering all types of MOs. Nonlinear differential equations of motion valid for all types of MOs with their respective solutions were presented, from which the relations for any certain type of MO are derived as special cases. …”
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Evaluation of the increased load bearing capacity of steel beams strengthened with pre-stressed FRP laminates by S. Bennati, D. Colonna, P.S. Valvo

“…The model is described by a set of differential equations with suitable boundary conditions. …”
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Nonlinear Dynamics of the High-Speed Rotating Plate by Minghui Yao, Li Ma, Wei Zhang

“…Galerkin approach is applied to discretize the partial differential governing equations of motion to ordinary differential equations. Asymptotic perturbation method is exploited to derive four-degree-of-freedom averaged equation for the case of 1 : 3 internal resonance-1/2 sub-harmonic resonance. …”
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An individual-level probabilistic model and solution for control of infectious diseases by Ye Xia

“…The model is related to the work of Fraser et al. on the same topic [1], which provides a population-level model using a combination of differential equations and probabilistic arguments. We show that our individual-level model has certain advantages. …”
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INFLUENCE OF THE TIME OF DISINHIBITION TO TRANSIENTS AND WEAR OF THE FRICTION LININGS IN AN ASYNCHRONOUS MOTOR by V. V. Solencov, V. V. Brel

“…Calculation of the system of differential equations was fulfilled by the Runge – Kutta method. …”
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In Silico Evolution of Gene Cooption in Pattern-Forming Gene Networks by Alexander V. Spirov, Marat A. Sabirov, David M. Holloway

“…Finally, we comment on how a differential equations (in contrast to Boolean) approach is necessary for addressing realistic continuous variation in biochemical parameters.…”
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Stability, Bifurcation, and a Pair of Conserved Quantities in a Simple Epidemic System with Reinfection for the Spread of Diseases Caused by Coronaviruses by Jorge Fernando Camacho, Cruz Vargas-De-León

“…In this paper, we study a modified SIRI model without vital dynamics, based on a system of nonlinear ordinary differential equations, for epidemics that exhibit partial immunity after infection, reinfection, and disease-induced death. …”
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