Numerical modelling in biosciences using delay differential equations

From MaRDI portal

Publication:1841955

Jump to:navigation, search

DOI10.1016/S0377-0427(00)00468-4zbMath0969.65124MaRDI QIDQ1841955

Fathalla A. Rihan, Gennadii A. Bocharov

Publication date: 7 October 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

physiology parameter estimation neural networks population dynamics delay differential equations nonlinear integro-differential equations immunology epidemiology numerical modelling cell kinetics biological systems retarded functional differential equations biosystem dynamics

Mathematics Subject Classification ID

Epidemiology (92D30) Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Neural networks for/in biological studies, artificial life and related topics (92B20) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Population dynamics (general) (92D25) Computational methods for problems pertaining to biology (92-08)

Related Items

Sensitivity analysis for dynamic systems with time-lags ⋮ Stochastic SIRC epidemic model with time-delay for COVID-19 ⋮ Time-varying delays in electrophysiological wave propagation along cardiac tissue and minimax control problems associated with uncertain bidomain type models ⋮ Cardiac memory phenomenon, time-fractional order nonlinear system and bidomain-torso type model in electrocardiology ⋮ Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay ⋮ Dissipativity of \(\theta\)-methods for nonlinear Volterra delay-integro-differential equations ⋮ Editorial: Applications of delay differential equations in biological systems ⋮ Dynamic optimal control of enhancing feedback treatment for a delayed fractional order predator-prey model ⋮ High order stable Runge-Kutta methods for nonlinear generalized pantograph equations on the geometric mesh ⋮ Accuracy of the Laplace transform method for linear neutral delay differential equations ⋮ Uniform ultimate boundedness of numerical solutions to nonlinear neutral delay differential equations ⋮ Stability of linear multistep methods for nonlinear neutral delay differential equations in Banach space ⋮ Convergence analysis of the homogeneous second order difference method for a singularly perturbed Volterra delay-integro-differential equation ⋮ A nonlinear delayed model for the immune response in the presence of viral mutation ⋮ A mathematical model of multiple delayed feedback control system of the gut microbiota--antibiotics injection controlled by measured metagenomic data ⋮ Convergence and stability analysis of the \({\theta}\)-method for delayed diffusion mathematical models ⋮ Galerkin-Arnoldi algorithm for stability analysis of time-periodic delay differential equations ⋮ Delay-induced bifurcations and chaos in a two-dimensional model for the immune response ⋮ Errors of linear multistep methods for singularly perturbed Volterra delay-integro-differential equations ⋮ Complete controllability and controllability for linear autonomous systems of neutral type ⋮ Stage-based interpolation Runge-Kutta methods for nonlinear Volterra functional differential equations ⋮ Contractivity properties of a class of linear multistep methods for nonlinear neutral delay differential equations ⋮ Classical theory of linear multistep methods for Volterra functional differential equations ⋮ Stability switching and chaos in a multiple delayed prey-predator model with fear effect and anti-predator behavior ⋮ Impact of time delay in perceptual decision-making: neuronal population modeling approach ⋮ Parametric sensitivity analysis of oscillatory delay systems with an application to gene regulation ⋮ On the positivity and zero crossings of solutions of stochastic Volterra integrodifferential equations ⋮ High-order collocation methods for singular Volterra functional equations of neutral type ⋮ Amplitude and frequency variation in nonlinear glucose dynamics with multiple delays via periodic perturbation ⋮ Stability analysis of general linear methods for nonlinear neutral delay differential equations ⋮ Rival approaches to mathematical modelling in immunology ⋮ Stochastic delay differential equations for genetic regulatory networks ⋮ Continuous neural identifier for uncertain nonlinear systems with time delays in the input signal ⋮ Stability and bifurcation analysis of a fractional order delay differential equation involving cubic nonlinearity ⋮ Stochastic delay differential equations: analysis and simulation studies ⋮ Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay ⋮ \(\mathrm{L}^p\)-calculus approach to the random autonomous linear differential equation with discrete delay ⋮ Identifying noise sources of time-delayed feedback systems ⋮ Comparison of mathematical frameworks for modeling erythropoiesis in the context of malaria infection ⋮ Method of exact difference schemes for the numerical solution of parameterized singularly perturbed problem ⋮ Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey ⋮ Stability analysis of the family of tumour angiogenesis models with distributed time delays ⋮ Efficient numerical approach for solving fractional partial differential equations with non-singular kernel derivatives ⋮ Periodic solutions of nonlinear delay differential equations using spectral element method ⋮ Maximum profile likelihood estimation of differential equation parameters through model based smoothing state estimates ⋮ Vector-valued stochastic delay equations -- a weak solution and its Markovian representation ⋮ Stability analysis of Volterra delay-integro-differential equations and their backward differentiation time discretization. ⋮ Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology ⋮ Oscillation criteria for delay and advanced differential equations with nonmonotone arguments ⋮ Stability analysis of one-leg methods for nonlinear neutral delay integrodifferential equations ⋮ Spectral Galerkin schemes for a class of multi-order fractional pantograph equations ⋮ Nonlinear stability of explicit and diagonally implicit Runge-Kutta methods for neutral delay differential equations in Banach space ⋮ High order explicit exponential Runge-Kutta methods for semilinear delay differential equations ⋮ Mathematical modeling and analysis of dynamic effects of multiple time-varying delays on electrophysiological wave propagation in the heart ⋮ Recovery of delay time from time series based on the nearest neighbor method ⋮ Kramers-Moyal expansion for stochastic differential equations with single and multiple delays: applications to financial physics and neurophysics ⋮ On \(A\)-stable one-leg methods for solving nonlinear Volterra functional differential equations ⋮ Nonlinear stability of one-leg methods for delay differential equations of neutral type ⋮ Delay differential model of one-predator two-prey system with Monod-Haldane and Holling type II functional responses ⋮ Oscillation analysis of numerical solutions for delay differential equations with real coefficients ⋮ Time-dependent solutions for stochastic systems with delays: perturbation theory and applications to financial physics ⋮ Dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations ⋮ Optimal disturbances of bistable time-delay systems modeling virus infections ⋮ On the numerical solution of nonlinear systems of Volterra integro-differential equations with delay arguments ⋮ Explicit exponential Runge-Kutta methods for semilinear parabolic delay differential equations ⋮ Stability of Runge-Kutta methods for neutral delay-integro-differential-algebraic system ⋮ Identifying and comparing states of time-delayed systems: phase diagrams and applications to human motor control systems ⋮ Delay- and noise-induced transitions: a case study for a Hongler model with time delay ⋮ Stochastic systems with delay: perturbation theory for second order statistics ⋮ Optimal convergence orders of fully geometric mesh one-leg methods for neutral differential equations with vanishing variable delay ⋮ Superconvergent interpolants for collocation methods applied to Volterra integro-differential equations with delay ⋮ On the one-leg methods for solving nonlinear neutral differential equations with variable delay ⋮ Stability of continuous Runge-Kutta-type methods for nonlinear neutral delay-differential equations ⋮ Chimera regimes in a ring of oscillators with local nonlinear interaction ⋮ Preserving stability implicit Euler method for nonlinear Volterra and neutral functional differential equations in Banach space ⋮ Non-Fickian delay reaction-diffusion equations: theoretical and numerical study ⋮ Analytical and numerical stability of nonlinear neutral delay integro-differential equations ⋮ Reconstruction of time-delayed feedback systems from time series ⋮ Numerical solution of a class of functional-differential equations using Jacobi pseudospectral method ⋮ Computational modelling with functional differential equations: identification, selection, and sensitivity ⋮ An analytical solution for a nonlinear time-delay model in biology ⋮ Dissipativity of Runge-Kutta methods for neutral delay differential equations with piecewise constant delay ⋮ Stability of fractional-order prey-predator system with time-delay and Monod-Haldane functional response ⋮ A finite-difference method for a singularly perturbed delay integro-differential equation ⋮ Stability conditions for singularly perturbed delay differential equations ⋮ Neural network solution of single-delay differential equations ⋮ Stability and Hopf bifurcation of three-species prey-predator system with time delays and allee effect ⋮ Synchronization of two coupled multimode oscillators with time-delayed feedback ⋮ Persistence and extinction for stochastic delay differential model of prey predator system with hunting cooperation in predators ⋮ Numerical modeling of fractional-order biological systems ⋮ Efficient numerical method for a model arising in biological stoichiometry of tumour dynamics ⋮ A new method based on the Laplace transform and Fourier series for solving linear neutral delay differential equations ⋮ Computational approaches to parameter estimation and model selection in immunology ⋮ Numerical bifurcation analysis of immunological models with time delays ⋮ Stability analysis of implicit-explicit \(\theta\)-methods for composite stiff neutral functional differential equations in Banach space ⋮ Stability analysis of numerical methods for linear neutral Volterra delay-integro-differential system ⋮ A model for the development of \textit{Aedes} (\textit{Stegomyia}) \textit{aegypti} as a function of the available food ⋮ Parameter estimation in nonlinear delayed feedback systems from noisy data ⋮ New approximations, and policy implications, from a delayed dynamic model of a fast pandemic ⋮ Stochastic delay differential equations of three-species prey-predator system with cooperation among prey species ⋮ Numerical Analysis of a Nonlinear Singularly Perturbed Delay Volterra Integro-Differential Equation on an Adaptive Grid ⋮ Delay-Dependent Stability of Linear Multistep Methods for Neutral Systems with Distributed Delays ⋮ VIM-Pad´e technique for solving nonlinear and delay initial value problems ⋮ Robust spectral treatment for time-fractional delay partial differential equations ⋮ Approximation of mild solutions of delay integro-differential equations on Banach spaces ⋮ Stability inequalities and numerical solution for neutral Volterra delay integro-differential equation ⋮ Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity ⋮ Atangana–Baleanu–Caputo differential equations with mixed delay terms and integral boundary conditions ⋮ A novel fitted method for a class of singularly perturbed differential-difference equations with small delay exhibiting twin layer or oscillatory behaviour ⋮ Time delays and economic profit in fractional differential‐algebraic predator–prey model ⋮ The impact of fear effect on the dynamics of a delayed predator–prey model with stage structure ⋮ Error estimate of BDF2 scheme on a Bakhvalov-type mesh for a singularly perturbed Volterra integro-differential equation ⋮ A priori and a posteriori error estimation for singularly perturbed delay integro-differential equations ⋮ Kramers’ turnover phenomenon in the spatial diffusion region ⋮ Transformations from Variable Delays to Constant Delays with Applications in Engineering and Biology ⋮ Dissipativity of θ-methods for a class of nonlinear neutral delay integro-differential equations ⋮ Numerical solution of delay integro‐differential equations by using Taylor collocation method ⋮ Multi-Step Maruyama Methods for Stochastic Delay Differential Equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Galerkin approximations with embedded boundary conditions for retarded delay differential equations ⋮ Viscosity Solutions to Delay Differential Equations in Demo-Economy ⋮ Second order evolution differential functional equations with infinite delay ⋮ Legendre wavelet solution of high order nonlinear ordinary delay differential equations ⋮ Numerical Solution of Second-Order Linear Delay Differential and Integro-Differential Equations by Using Taylor Collocation Method ⋮ Delay differential model for tumour–immune dynamics with HIV infection of CD4⁺T-cells ⋮ Richardson Extrapolation Method on an Adaptive Grid for Singularly Perturbed Volterra Integro-Differential Equations ⋮ Unnamed Item ⋮ k_p-stable regions in the space of time delay and PI controller coefficients ⋮ Piecewise Spectral Collocation Method for Second Order Volterra Integro-Differential Equations with Nonvanishing Delay ⋮ Dissipativity ofθ-methods for a class of advection–reaction–diffusion equations with both fixed and distributed delays ⋮ A novel second-order fitted computational method for a singularly perturbed Volterra integro-differential equation

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1841955&oldid=14217740"