Influence of weak injection on spatiotemporal instabilities in a broad-area vertical-cavity semiconductor laser by E.A. Yarunova, A.A. Krents, N.E. Molevich

“…The results are confirmed by the numerical solution of a system of differential equations. It is shown that the suppression of the modulation instability can be achieved by injecting into the resonator an external low-amplitude optical radiation.…”
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Study on Synchronization of Two Eccentric Rotors Driven by Hydraulic Motors in One Vibrating System by Tianxia Zhang, Bangchun Wen, Jian Fan

“…In this article the synchronization of two eccentric rotors driven by hydraulic motors (TERDHM) in one vibrating system is studied. The differential equations of TERDHM motion are derived, and the synchronous and stable rotating conditions of TERDHM are established. …”
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A New Fractional Model for Cancer Therapy with M1 Oncolytic Virus by Majda El Younoussi, Zakaria Hajhouji, Khalid Hattaf, Noura Yousfi

“…The aim of this work is to propose and analyze a new mathematical model formulated by fractional differential equations (FDEs) that describes the dynamics of oncolytic M1 virotherapy. …”
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On fractional Pennes bio-heat equation using Legendre collocation method by Arvind Kumar Mishra, Sushil Kumar, Ajay Kumar Shukla

“…The best feature of the proposed technique is the conversion of fractional-order differential equations into a set of algebraic systems and the ability to approximate both spatial and temporal coordinates with a single basis. …”
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Numerical Solutions of a Variable-Order Fractional Financial System by Shichang Ma, Yufeng Xu, Wei Yue

“…Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the method is also estimated numerically. …”
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On a Partial q-Analog of a Singularly Perturbed Problem with Fuchsian and Irregular Time Singularities by Stephane Malek

“…A family of linear singularly perturbed difference differential equations is examined. These equations stand for an analog of singularly perturbed PDEs with irregular and Fuchsian singularities in the complex domain recently investigated by A. …”
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On the Solutions of Okubo-Type Systems by Galina Filipuk, Alberto Lastra

“…Röscheisen, J. Differential Equations, 2009).…”
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Novel exact solutions for PDEs with mixed boundary conditions by Mark Craddock, Martino Grasselli, Andrea Mazzoran

“…Abstract We develop methods for the solution of inhomogeneous Robin-type boundary value problems (BVPs) that arise for certain linear parabolic partial differential equations (PDEs) on a half-line, as well as a second-order generalization. …”
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Parametrically excited nonlinear systems: a comparison of two methods by A. F. El-Bassiouny

“…Two approximate methods (the multiple scales and the generalized synchronization) are used to construct a first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases. …”
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Optimization using response surface methodology for Eyring-powell fluid flow with Cattaneo-Christov heat flux and cross diffusion effects by Pradeep Kumar, Vidhya K G, Felicita Almeida, Qasem Al-Mdallal

“…Using similarity transformations, the governing partial differential equations are converted into ordinary differential equations, which are numerically solved using the Runge-Kutta-Fehlberg 4th-5th order method. …”
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Stratifications and foliations in phase portraits of gene network models by V. P. Golubyatnikov, A. A. Akinshin, N. B. Ayupova, L. S. Minushkina

“…Periodic processes of gene network functioning are described with good precision by periodic trajectories (limit cycles) of multidimensional systems of kinetic-type differential equations. In the literature, such systems are often called dynamical, they are composed according to schemes of positive and negative feedback between components of these networks. …”
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Birth Rate Effects on an Age-Structured Predator-Prey Model with Cannibalism in the Prey by Francisco J. Solis, Roberto A. Ku-Carrillo

“…It consists of systems of m ordinary differential equations, where m is a parameter associated with new proposed prey birth rates. …”
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A Fixed Point Technique for Set-Valued Contractions with Supportive Applications by Hasanen A. Hammad, Manuel De la Sen

“…Finally, the theoretical results are used to study the existence of the solution of Fredholm integral equation which arises from the damped harmonic oscillator, to study initial value problem which arises from Newton’s law of cooling and to study infinite systems of fractional ordinary differential equations (ODEs).…”
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Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays by Huitao Zhao, Yiping Lin, Yunxian Dai

“…Using a global Hopf bifurcation result of Wu (1998) for functional differential equations, the global existence of the periodic solutions is obtained. …”
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A mathematical model of stem cell regeneration with epigenetic state transitions by Qiaojun Situ, Jinzhi Lei

“…The dynamics of the subpopulations are modeled by a set of ordinary differential equations in which epigenetic state transition in cell division is given by the transition probability. …”
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Superposed Incremental Deformations of an Elastic Solid Reinforced with Fibers Resistant to Extension and Flexure by Chun IL Kim

“…In particular, the complete systems of differential equations are obtained for the cases of Neo-Hookean and Mooney–Rivlin types of materials from which analytical solutions can be obtained.…”
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Contact Characteristic Analysis of Thrust Needle Bearing by Liu Peng, Zhang Wenhu, Zhao Gang, Li Tiefeng, Cui Wenbin, Yang Chao

“…Based on the dynamics of rolling bearing,an improved slice method is used to solve the problem of needle-race contact,and the dynamics differential equations are established and solved by Predicting-Correcting GSTIFF（ Gear Stiff） integer algorithm with variable step. …”
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Dynamical Modelling of Bone Formation and Resorption under Impulsive Estrogen Supplement: Effects of Parathyroid Hormone and Prolactin by Supassorn Aekthong, Chontita Rattanakul

“…A system of impulsive differential equations is developed in this paper in order to investigate the effects of parathyroid hormone and prolactin on bone-forming cells, namely, osteoblasts, and bone-resorbing cells, namely, osteoclasts, under the impulsive estrogen supplement. …”
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Torsional Vibrations at Guide-Vane Shaft of Pump–Turbine Model by Andrej Predin

“…The mathematical models for theoretical torsional vibration prediction formulated using linear and nonlinear differential equations are presented. The results of theoretical calculations are compared with measurement results. …”
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Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions by F. A. Rihan, M. Safan, M. A. Abdeen, D. Abdel Rahman

“…We provide a family of ordinary and delay differential equations to model the dynamics of tumor-growth and immunotherapy interactions. …”
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