Photosynthesis as a discrete biochemical process by M. Štetina, J. KrempaskÝ

“…Transforming known phenomenological differential equations describing the photosynthesis into the discrete formalism it is possible to demonstrate that by change of control parameters such equations generate the very well known Feigenbaum‘s scenario of the duplication of states including the possibility of the transition into a chaotic regime. …”
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Oscillation for Forced Second-Order Impulsive Nonlinear Dynamic Equations on Time Scales by Mugen Huang, Kunwen Wen

“…As the unification and development of impulsive differential equations and difference equations, impulsive dynamic equations on time scales are a powerful tool to simulate the natural and social phenomena. …”
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Construction of a Class of Copula Using the Finite Difference Method by Remi Guillaume Bagré, Frédéric Béré, Vini Yves Bernadin Loyara

“…For this, we use the finite difference method which is a common technique for finding approximate solutions of partial differential equations which consists in solving a system of relations (numerical scheme) linking the values of the unknown functions at certain points sufficiently close to each other.…”
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Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation by Dang Quang A., Nguyen Van Thien

“…Solving boundary value problems (BVPs) for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. …”
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Two-Degree Vibration Analysis of a Horizontal Axis Turbine Blade by Finite Differential Methods by Youfeng Zhu, Hongyu Zang, Xiaofei Kong, Peng Ban

“…Two-degree vibration partial differential equations of large horizontal axis turbine blades were established by Kallesøe’s model and Greenberg unsteady aerodynamic theory. …”
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Ecoepidemiological Model and Analysis of MSV Disease Transmission Dynamics in Maize Plant by Haileyesus Tessema Alemneh, Oluwole Daniel Makinde, David Mwangi Theuri

“…In this paper, an ecoepidemiological deterministic model for the transmission dynamics of maize streak virus (MSV) disease in maize plant is proposed and analysed qualitatively using the stability theory of differential equations.The basic reproduction number with respect to the MSV free equilibrium is obtained using next generation matrix approach. …”
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On the Exact Solutions of Nonlinear Potential Yu–Toda–Sasa–Fukuyama Equation by Different Methods by Qinghao Zhu, Jianming Qi

“…It is observed that the extended complex method and G′/G-expansion method are reliable and will be used extensively to seek for exact solutions of any other nonlinear partial differential equations (NPDEs).…”
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Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus by Uğur Kadak, Muharrem Özlük

“…In this paper, the well-known Runge-Kutta method for ordinary differential equations is developed in the frameworks of non-Newtonian calculus given in generalized form and then tested for different generating functions. …”
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Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric Equations by Rodica D. Costin, Marina David

“…As an application it is shown that nonhomogeneous differential equations of hypergeometric type do generically have a unique solution which is analytic at both singular points in C.…”
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Convergence of the solutions for the equation x(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛) by Anthony Uyi Afuwape

“…This paper is concerned with differential equations of the formx(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛)where a, b are positive constants and the functions g, h and p are continuous in their respective arguments, with the function h not necessarily differentiable. …”
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Convexity of the Set of Fixed Points Generated by Some Control Systems by Vadim Azhmyakov

“…We study closed-loop and open-loop controllable dynamical systems governed by ordinary differential equations (ODEs) and establish convexity of the set of trajectories. …”
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Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays

“…The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. …”
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Positive Solutions of a General Discrete Dirichlet Boundary Value Problem by Xinfu Li, Guang Zhang

“…To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different.…”
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A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution by D. P. Siu, G. S. Ladde

“…The system under investigation is a first-order linear nonhomogeneous system of Itô-Doob type stochastic differential equations with switching coefficients. The switching of the system is governed by a discrete dynamic which is monitored by a non-homogeneous Poisson process. …”
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Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis by Ravindra Rao, Jagan Mohan Jonnalagadda

“…We study the existence and uniqueness of solutions to a particular class of two-point boundary value problems involving fourth-order ordinary differential equations. Such problems have exciting applications for modeling the deflections of beams. …”
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Study of Hybrid Problems under Exponential Type Fractional-Order Derivatives by Mohammed S. Abdo, Sahar Ahmed Idris, M. Daher Albalwi, Tomadir Ahmed Idris

“…In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. …”
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Bifurcation Analysis and Single Traveling Wave Solutions of the Variable-Coefficient Davey–Stewartson System by Tianyong Han, Jiajin Wen, Zhao Li

“…By employing the traveling wave transformation, the variable-coefficient Davey–Stewartson system is reduced to two-dimensional nonlinear ordinary differential equations. On the one hand, we use the bifurcation theory of planar dynamical systems to draw the phase diagram of the variable-coefficient Davey–Stewartson system. …”
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Mathematical Modeling of Commensalism Between Two Species with Limited Resources. by Namutebi, Aminah

“…This model is characterized by a pair of first-order non-linear coupled differential equations. All four equilibrium points of the model are identified and the nature of stability of the four equilibrium points is discussed using the Jacobian and trace determinant method. …”
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Differential Subordinations of Arithmetic and Geometric Means of Some Functionals Related to a Sector by A. Lecko, M. Lecko

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Thermal radiation and thermo-diffusion in Casson-ferrofluid over a magnetized porous surface: RSM analysis by S. Manjunatha, J. Santhosh Kumar, Khalil Ur Rehman, Wasfi Shatanawi, S.V.K. Varma

“…Similarity transformations convert the flow model's governing nonlinear coupled partial differential equations into ordinary coupled differential equations. …”
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