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Search · four archives
21 papers · ranked by Valyu relevance
A. R. Humphries, A. S. Eremin, Z. Wang
Delays are ubiquitous in applied problems, but often do not arise as the simple constant discrete delays that analysts and numerical analysts like to treat. In this chapter we show how state-dependent delays arise naturally when modeling and the consequences that follow. We treat discrete state-dependent delays, and…
Wu Hsiung Wu, Feng Sheng Wang, Maw Shang Chang
Background Mathematical modeling has been applied to the study and analysis of complex biological systems for a long time. Some processes in biological systems, such as the gene expression and feedback control in signal transduction networks, involve a time delay. These systems are represented as delay differential…
H. F. Wang, Yuxing Chen, Sirong Cao, Xiaoli Wang + 1 more
in Delay Differential Equations Authors: ['H. F. Wang' 'Yuxing Chen' 'Sirong Cao' 'Xiaoli Wang' 'Qiang Liu'] We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of…
Dario Schöbi, Cao-Tri Do, Stefan Frässle, Marc Tittgemeyer + 2 more
Dynamic causal models (DCMs) of electrophysiological data allow, in principle, for inference on hidden, bulk synaptic function in neural circuits. The directed influences between the neuronal elements of modeled circuits are subject to delays due to the finite transmission speed of axonal connections. Ordinary…
Titus Ifeanyi Chinebu, Kennedy Chinedu Okafor, Cajetan Uwatoronye Nwadinigwe, Juliet Onyinye Nwigwe + 4 more
Recovery from knee replacement surgery in conventional orthopaedic healthcare systems can be delayed due to high costs, pain, limited monitoring, and insufficient follow-up, which may hinder early detection of poor healing and inflammation. This study presents a smart orthopaedic healthcare model for knee replacement…
Brahim Benhammouda, Hector Vazquez-Leal
This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful…
Leping Sun
This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true.
Shuo-Tsung Chen, Shun‐Pin Hsu, Huang‐Nan Huang, Binyan Yang
In this work, we establish the response of scalar systems with multiple discrete delays based on the Laplace transform. The time response function is expressed as the sum of infinite series of exponentials acting on eigenvalues inside countable branches of the Lambert W functions. Eigenvalues in each branch of Lambert…
Federico Gollinucci, Enrico Ortu, Lamberto Rondoni, Zhigang Zheng
The exact response theory, also known as Transient Time Correlation Function formalism, is a powerful method concerning how observables respond to a given perturbation of the dynamics of the systems of interest, and it extends linear response theory to generic (autonomous) dynamical systems. Its main ingredient is the…
Christopher N. Angstmann, Stuart-James M. Burney, Daniel Han, B. I. Henry + 1 more
'B. I. Henry' 'Zhijie Xu'] Exact solutions are derived for a time-delay advection equation and a fractional-order time-delay advection equation with a time-delay in the spatial derivative. Solutions are obtained, for arbitrary separable initial conditions, by incorporating recently introduced delay functions in a…
A.V. Paraskevov
Starting with the classical biophysical Morris-Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the…
Mathew O. Aibinu, Surendra Thakur, Sibusiso Moyo
a Institute for Systems Science & KZN E-Skill CoLab, Durban University of Technology, Durban 4000, South Africa bDSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa cNational Institute for Theoretical and Computational Sciences (NITheCS), South Africa dKZN E-Skill CoLab…
Andrei D. Polyanin, Alexei I. Zhurov
where u = u(x, t), w = u(x, t−τ), and τ is the delay time. The method is based on searching for solutions in the form u = PN n=1 ξn(x)ηn(t), where the functions ξn(x) and ηn(t) are determined from additional functional constraints (which are difference or functional equations) and the original delay partial…
Shakti Nath Singh, Athokpam Langlen Chanu, Md. Zubbair Malik, R.K. Brojen Singh
Delay is everywhere, no matter how small or big it is. Experimental evidences show the existence and importance of time delayed reactions specially in biological systems. The role of delay is found to be multifunctional and is seemed to be system dependent. The analytically solved P(X, t) of gene regulatory process…
Pushpendra Kumar, Dumitru Baleanu, Vedat Suat Erturk, Mustafa Inc + 1 more
'V. Govindaraj'] We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point…
Vanessa Steindorf, Sergio Oliva, Jianhong Wu
Dengue fever is endemic in tropical and sub-tropical countries, and some of the important features of Dengue fever spread continues to pose challenges for mathematical modelling. Here, we propose a system of integro-differential equations (IDE) to study the disease transmission dynamics that involves multiserotypes and…
Marcella M. Gomez, Richard M. Murray, Matthew R. Bennett
Delays in gene networks result from the sequential nature of protein assembly. However, it is unclear how models of gene networks that use delays should be modified when considering time-dependent changes in temperature. This is important, as delay is often used in models of genetic oscillators that can be entrained by…
Corentin Briat, Mustafa Khammash
Delays are an important phenomenon arising in a wide variety of real world systems. They occur in biological models because of diffusion effects or as simplifying modeling elements. We propose here to consider delayed stochastic reaction networks. The difficulty here lies in the fact that the state-space of a delayed…
Justin Eilertsen, Santiago Schnell
As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis-Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this…
Authors not listed
We develop a control-oriented model for manipulating calcium carbonate (CaCO3) precipitation through pH and/or dissolved CO2(aq) adjustments in a semi-batch process. We present two open-loop control strategies: first, a closed-form optimal control solution derived via Pontryagin’s Minimum Principle; and second, an…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
The determination of a substrate or enzyme activity by coupling of one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course…