Differentiability of perturbed semigroups and delay semigroups by Batty, C

“…We also give a brief account of the consequences for asymptotics of individual mild solutions of abstract Cauchy problems and delay differential equations.…”

Lyapunov Functions to Caputo Fractional Neural Networks with Time-Varying Delays by Ravi Agarwal, Snezhana Hristova, Donal O’Regan

“…In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. …”
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Existence and stability of traveling waves in parabolic systems of differential equations with weak diffusion by I.I. Klevchuk

“…We use bifurcation theory for delay differential equations and quasilinear parabolic equations. …”
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Oncolytic potency and reduced virus tumor-specificity in oncolytic virotherapy. A mathematical modelling approach. by Khaphetsi Joseph Mahasa, Amina Eladdadi, Lisette de Pillis, Rachid Ouifki

“…The model consists of a system of delay differential equations with one (discrete) delay. We derive the model's basic reproductive number within tumor and normal cell populations and use their ratio as a metric for virus tumor-specificity. …”
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Nonlinear phase-amplitude reduction of delay-induced oscillations by Kiyoshi Kotani, Yutaro Ogawa, Sho Shirasaka, Akihiko Akao, Yasuhiko Jimbo, Hiroya Nakao

“…Phase reduction theory for limit-cycle oscillators described by delay-differential equations (DDEs) has been developed to analyze their synchronization properties, but it is applicable only when the perturbation applied to the oscillator is sufficiently weak. …”
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A Generalized Wirtinger's Inequality with Applications to a Class of Ordinary Differential Equations by Cheng Rong, Zhang Dongfeng

“…Then, applying the inequality, we study estimates for lower bounds of periods of periodic solutions for a class of delay differential equations <inline-formula> <graphic file="1029-242X-2009-710475-i1.gif"/></inline-formula>, and <inline-formula> <graphic file="1029-242X-2009-710475-i2.gif"/></inline-formula>, where <inline-formula> <graphic file="1029-242X-2009-710475-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2009-710475-i4.gif"/></inline-formula>, and <inline-formula> <graphic file="1029-242X-2009-710475-i5.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-710475-i6.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2009-710475-i7.gif"/></inline-formula> are two given constants. …”
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Finite-time Stability, Dissipativity and Passivity Analysis of Discrete-time Neural Networks Time-varying Delays by Porpattama Hammachukiattikul

“…The neural network time-varying delay was described as the dynamic properties of a neural cell, including neural functional and neural delay differential equations. The differential expression explains the derivative term of current and past state. …”
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Bifurcations in a Plant-Pollinator Model with Multiple Delays by Long Li, Yanxia Zhang, Jianfei Yao, Xiuxing Wu

“…Under the condition that two delays are not equal, some explicit formulas for determining the direction of Hopf bifurcation and some conditions for the stability of periodic solutions of bifurcation are obtained for delay differential equations by using the theory of norm form and the theorem of center manifold. …”
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Population dynamics of a Salmonella lytic phage and its host: implications of the host bacterial growth rate in modelling. by Sílvio B Santos, Carla Carvalho, Joana Azeredo, Eugénio C Ferreira

“…We have developed an unstructured mathematical model using delay-differential equations to predict the interactions between a broad-host-range Salmonella phage and its pathogenic host. …”
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Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays by Eide, R, Kruase, A, Fadai, N, Van Gorder, R

“…The population interactions are modelled by a system of delay differential equations, where travel time is incorporated as discrete delay in the network diffusion term in order to model time taken to migrate between spatial regions. …”

Complex global dynamics of conditionally stable slopes: effect of initial conditions by D. Prekrat, N. K. Todorović-Vasović, N. Vasović, S. Kostić, S. Kostić

“…The time evolution of the studied model, which is governed by a system of stochastic delay differential equations, is analyzed in the mean-field approximation, which qualitatively exhibits the same dynamics as the initial model. …”
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Metastable spiking networks in the replica-mean-field limit. by Luyan Yu, Thibaud O Taillefumier

“…Technically, these stationary rates are determined as the solutions of a set of delayed differential equations under certain regularity conditions that any physical solutions shall satisfy. …”
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Quantitative analysis of the effective functional structure in yeast glycolysis. by Ildefonso M De la Fuente, Jesus M Cortes

“…The data were obtained by means of a yeast glycolytic model formed by three delay differential equations where the enzymatic rate equations of the irreversible stages have been explicitly considered. …”
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Dynamics of an epidemic model with relapse over a two-patch environment by Dongxue Yan, Xingfu Zou

“…The model is given by a system of delay differential equations with a fixed delay accounting for the fixed constant relapse time and a non-local term caused by the mobility of the individuals during the recovered period. …”
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Impact of fiscal policy delays on the system dynamics of IS-LM model: A mathematical model approach by Akanksha Rajpal, Sumit Kaur Bhatia, Praveen Kumar

“…Delays in fiscal policy reside either in taxation or in government expenditure.The former delay refers to the time lag between when taxes are accrued and when they are paid.And the latter delay refers to the amount of time that passes between making a purchasing decision and making a purchase.This work combines both these delays into a business cycle model, namely the IS-LM model.Firstly, two mathematical models, Model A and Model B, based on delayed differential equations, are constructed with non-linear and linear functional forms respectively, for investment and liquidity preference.After that, a steady-state solution is computed, which is unique in both instances.Linear stability analysis is performed around the equilibrium point in both the models.Also, when the delay reaches a critical point, Hopf bifurcation occurs.The switch in the stability of equilibrium point for both the models is also discussed.Lastly, numerical simulations are performed to validate our analysis.In both the models, adding a correct mix of time delays aids in maintaining or regaining the stability of equilibria.Also, the effect of relationship between the parameters like tax rate and share of delayed tax revenue is closely scrutinized to assess the stability of the system, which is not cogitated before.…”
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Low level viral persistence after infection with LCMV: a quantitative insight through numerical bifurcation analysis. by Luzyanina, T, Engelborghs, K, Ehl, S, Klenerman, P, Bocharov, G

“…This model, described by a non-linear system of delay differential equations (DDEs), is studied using numerical bifurcation analysis techniques for DDEs. …”

Some problems in abstract stochastic differential equations on Banach spaces by Crewe, P

“…Such problems are also known as functional differential equations or delay differential equations. We show that the methods of van Neerven et al. extend to such problems if the initial history of the system lies in a space of a type introduced by Hale and Kato. …”

Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction. by Beguerisse-Díaz, M, Desikan, R, Barahona, M

“…Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction.…”

Instability Induced by Random Background Noise in a Delay Model of Landslide Dynamics by Srđan Kostić, Nebojša Vasović, Kristina Todorović, Dragan Prekrat

“…The proposed mechanical model is described in the form of a nonlinear dynamical system: a set of stochastic delay-differential equations. The solution of such a system is enabled by the introduction of mean-field approximation, which resulted in a mean-field approximated model whose dynamics are qualitatively the same as the dynamics of the starting stochastic system. …”
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Hopf bifurcation exploration and control technique in a predator-prey system incorporating delay by Wei Ou, Changjin Xu, Qingyi Cui, Yicheng Pang, Zixin Liu, Jianwei Shen, Muhammad Zafarullah Baber, Muhammad Farman, Shabir Ahmad

“…With the aid of bifurcation theorem and stability theory of delayed differential equations, we gain the parameter conditions on the emergence of stability and bifurcation phenomenon of the two formulated delayed predator-prey systems. …”
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