Distributed Delay Differential Equation Representations of Cyclic Differential Equations [PDF]
SIAM Journal on Applied Mathematics, 2021 Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is equivalent to an Erlang distributed delay differential equation (DDE).
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Neural Delay Differential Equations
, 2021 Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been successfully developed for conquering some limitations emergent in application of the original framework.
Zhu, Qunxi, Guo, Yao, Lin, Wei
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On nonlinear delay differential equations [PDF]
Transactions of the American Mathematical Society, 1994 We examine qualitative behaviour of delay differential equations of the form \[ y ′ ( t ) = h ( y ( t ) , y ( q t ) ) , y ( 0 ) = y 0
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, 2015 This is a short presentation on the topic of 'Delay Differential Equations'. In the latter part, I discuss a DDE system - the Mackey-Glass equation, in some detail (phase diagrams, bifurcations, chaos).
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Parabolic differential equations with bounded delay
Journal of Evolution Equations, 2022 AbstractWe show the continuous dependence of solutions of linear nonautonomous second-order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-* topology of delay coefficients is required. The results are important in the applications of the theory of
Marek Kryspin, Janusz Mierczyński
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Numerical solution of neutral delay differential equations using orthogonal neural network. [PDF]
Sci Rep, 2023 Vinodbhai CD, Dubey S.
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Numerical methods and hypoexponential approximations for gamma distributed delay differential equations. [PDF]
IMA J Appl Math, 2022 Cassidy T +3 more
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An Efficient Numerical Scheme for Solving a Fractional-Order System of Delay Differential Equations. [PDF]
Int J Appl Comput Math, 2022 Kumar M.
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Stability in distribution for uncertain delay differential equations based on new Lipschitz condition. [PDF]
J Ambient Intell Humaniz Comput, 2022 Gao Y, Jia L.
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Delay differential equations for the spatially resolved simulation of epidemics with specific application to COVID-19. [PDF]
Math Methods Appl Sci, 2022 Guglielmi N, Iacomini E, Viguerie A.
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