Modelling the cancer growth process by stochastic delay diffferential equations under verhults and gompertz's law by Mazma Syahidatul Ayuni, Mazlan, Norhayati, Rosli, Nina Suhaity, Azmi

“…The growth process under two different laws which are Verhults and Gompertz’s law are considered, thus leading to stochastic delay differential equations (SDDEs) of logistic and Gompertzian, respectively. …”
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Stability of numerical method for semi-linear stochastic pantograph differential equations by Yu Zhang, Longsuo Li

“…Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. …”
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Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices by Oleksandr Boichuk, Milan Medved, Valerii Zhuravliov

“…Moreover, a family of linearly independent solutions in an explicit general analytic form is constructed under the assumption that the number of boundary conditions (defined by a dimension of linear vector functional) do not coincide with the number of unknowns of the system of the delay differential equations. The proof of this result is based on a representation of solutions by using so-called multi-delayed matrix exponential and a method of a pseudo-inverse matrix of the Moore-Penrose type.…”
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Stability of a general delayed virus dynamics model with humoral immunity and cellular infection by A. M. Elaiw, A. A. Raezah, A. S. Alofi

“…The model is a four dimensional system of delay differential equations where the production and removal rates of the virus and cells are given by general nonlinear functions. …”
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Modelling and optimization for palm oil plantation management by Banitalebi, A., Aziz, M. I. A., Aziz, Z. A., Nasir, N.

“…A system of delay differential equations is developed to study the behaviour of palm oil plantation. …”

Direct estimation of the parameters of a delayed, intermittent activation feedback model of postural sway during quiet standing. by Kevin L McKee, Michael C Neale

“…A Kalman-Filter framework was designed to directly estimate from experimental data the parameters of the model's stochastic delay differential equations with discrete dynamic switching conditions. …”
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Stochastic Modeling of Plant Virus Propagation with Biological Control by Benito Chen-Charpentier

“…The model is written using delay differential equations. However, it can also be expressed in terms of biochemical reactions, which is more realistic for small populations. …”
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A Generalized Wirtinger's Inequality with Applications to a Class of Ordinary Differential Equations by Rong Cheng, Dongfeng Zhang

“…Then, applying the inequality, we study estimates for lower bounds of periods of periodic solutions for a class of delay differential equations x˙(t)=−∑k=1nf(x(t−kr)), and x˙(t)=−∑k=1ng(t,x(t−ks)), where x∈ℝp, f∈C(ℝp,ℝp), and g∈C(ℝ×ℝp,ℝp) and r>0, s>0 are two given constants. …”
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Effects of Helix Angle Variations on Stability of Low Immersion Milling by B. Moetakef Imani, Kazemi Nasrabadi, Kazemi Sadeghi

“…Time Finite Element Analysis (TFEA) is suggested for an approximate solution for delayed differential equations encountered during interrupted milling. …”
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Features of the Computational Implementation of the Algorithm for Estimating the Lyapunov Exponents of Systems with Delay by Vladimir E. Goryunov

“…We consider the computational implementation of the algorithm for Lyapunov exponents spectrum numerical estimation for delay differential equations. It is known that for such systems, as well as for boundary value problems, it is not possible to prove the well-known Oseledets theorem which allows us to calculate the required parameters very efficiently. …”
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A efficient analytical approach for nonlinear system of advanced Lorenz model by Barde, Aminu, Maan, Normah

“…The method combines the Natural transform and Homotopy analysis method, and it’s have been suggested for the solution of different types of nonlinear systems of delay differential equations. This technique gives solution in a series form where the He’s polynomial is adjusted for the series calculation of nonlinear terms of Lorenz system. …”

Reduction of Linear Functional Systems using Fuhrmann's Equivalence by Mohamed S. Boudellioua

“…Functional systems arise in the treatment of systems of partial differential equations, delay-differential equations, multidimensional equations, etc. …”
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Boundedness criteria for a class of second order nonlinear differential equations with delay by Daniel O. Adams, Mathew O. Omeike, Idowu A. Osinuga, Biodun S. Badmus

“…We consider certain class of second order nonlinear nonautonomous delay differential equations of the form a(t)x^{\prime\prime} + b(t)g(x,x^\prime) + c(t)h(x(t-r))m(x^\prime) = p(t,x,x^\prime) and (a(t)x^\prime)^\prime+ b(t)g(x,x^\prime) + c(t)h(x(t-r))m(x^\prime) = p(t,x,x^\prime), where $a$, $b$, $c$, $g$, $h$, $m$ and $p$ are real valued functions which depend at most on the arguments displayed explicitly and $r$ is a positive constant. …”
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Time lag analysis of novel arithmetic modeling in breast cancer by Kalyan Das, Ranjith Kumar, Pankaj Taneja, M Lutfor Rahman

“…In this paper, a mathematical model which considers population dynamics among infected and uninfected cancer tumor cells has been proposed. Delay differential equations have been utilized to demonstrate the framework to consider the periods of the cell cycle. …”
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Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments by Zonghong Feng, Yong Wang, Xin Ma

“…Abstract It is well known that differential equations with piecewise constant arguments is a class of functional differential equations, which has fascinated many scholars in recent years. These delay differential equations have been successfully applied to diverse models in real life, especially in biology, physics, economics, etc. …”
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Stability Analysis in Milling Based on the Localized Differential Quadrature Method by Yonggang Mei, Bingbing He, Shangwen He, Xin Ren

“…The milling process, considering the regeneration effect, is modeled using linear periodic delay differential equations (DDE), then the state transition matrix during the adjacent cutting period is constructed based on the LDQM, and finally, the stability of the milling process is obtained based on the Floquet theory. …”
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A Systematic Review on the Solution Methodology of Singularly Perturbed Differential Difference Equations by Gemechis File Duressa, Imiru Takele Daba, Chernet Tuge Deressa

“…The review covered singularly perturbed ordinary delay differential equations with small or large negative shift(s), singularly perturbed ordinary differential–differential equations with mixed shift(s), singularly perturbed delay partial differential equations with small or large negative shift(s) and singularly perturbed partial differential–difference equations of the mixed type. …”
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Numerical solution for a family of delay functional differential equations using step by step Tau approximations by René Escalante

“…We use the segmented formulation of the Tau method to approximate the solutions of a family of linear and nonlinear neutral delay differential equations a₁(t) y'(t) = y(t)[a₂(t)] y(t-τ) + a₃(t) y'(t-τ) + a₄(t)] + a₅(t) y(t-τ) + a₆(t) y'(t-τ) + a₇(t), t ≥ 0 y(t) = Ψ(t), t ≤ 0 which represents, for particular values of a_i(t), i=1,7, and τ, functional differential equations that arise in a natural way in different areas of applied mathematics. …”
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A stage-structured predator-prey si model with disease in the prey and impulsive effects by Tongqian Zhang, Xinzhu Meng, Yi Song, Tonghua Zhang

“…Firstly, we use analytical techniques for impulsive delay differential equations to obtain the conditions for global attractivity of the ‘pest-free’ periodic solution and permanence of the population model. …”
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Analysis of a dengue disease transmission model without immunity by Yaacob, Yusof

“…Taking the incubation period into consideration, the model without immunity gives rise to a two-dimensional delay differential equations. The presence of the delay seems to destabilise the dynamics…”
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