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Showing 1 to 20 of 26 for “"Delay Differential Equations"”.
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Difference Methods for Stiff Delay Differential Equations
Delay differential equations of the form y'(t) = f(y(t), z(t)), where z(t) = {y(,1)((alpha)(,1)(y(t))),..., y(,n)((alpha)(,n)(y(t)))}('T) and (alpha)(,i)(y(t)) (LESSTHEQ) t arise in many scientific and engineering fields when transport lags and propagation times are physically significant in a …
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Fitted numerical methods for delay differential equations arising in biology
Fitted Numerical Methods for Delay Di erential Equations Arising in Biology E.B.M. Bashier PhD thesis, Department of Mathematics and Applied Mathematics,Faculty of Natural Sciences, University of the Western Cape. This thesis deals with the design and analysis of tted numerical methods for some …
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Parameter Estimation for Delay Differential Equations: A New Galerkin Approximation Framework
Delay differential equations with discrete and/or distributed delays are widely used in many applied fields, including mathematical biology, climate science, and engineering. These equations contain free parameters and integral kernels that must be optimized to fit the dynamics of the physical …
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Role of delay differential equations in modelling low level HIV viral load
… for therapy removal are limited. Thus a set of delay differential models are designed, which account for previously overlooked important features of intracellular delay and HIV latency. Incorporation of these features requires additional model components, leading to a rapid increase in …
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Output Regulation of Systems Governed by Delay Differential Equations: Approximations and Robustness
… and disturbance rejection of systems governed by delay differential equations. It is well known that geometric regulation can be highly sensitive to system parameters and hence such designs are not always robust. In particular, when employing numerical approximations to delay systems, the …
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Explosions and unbounded growth in nonlinear delay differential equations: Numerical and asymptotic analysis
… nonlinear dierential equation with a fixed delay, and examines whether the properties of this equation can be replicated by an appropriate discretisation. We begin by considering equations for which the solution explodes in finite time. Existing work on such explosive equations has dealt …
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Galerkin Approximations of General Delay Differential Equations with Multiple Discrete or Distributed Delays
Delay differential equations (DDEs) are often used to model systems with time-delayed effects, and they have found applications in fields such as climate dynamics, biosciences, engineering, and control theory. In contrast to ordinary differential equations (ODEs), the phase space associated even …
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Random perturbations of delay differential equations at the verge of instability and periodically driven nonlinear oscillators
… the effect of small noise perturbations on delay differential equations (DDE) whose fixed point is on the verge of instability. With appropriate scaling of coordinates, the dynamics close to the fixed point can be cast in the form of a linear DDE perturbed by small noise and small …
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Volterra Systems with Realizable Kernels
… Runge-Kutta method for solving Volterra integro-differential equations and Volterra delay differential equations. The internal state method requires the kernel of the Volterra integral to be realizable as an impulse response function. We discover that when applicable, the internal state method is …
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Modelling the Impact of Climate Change on the Polar Bear Population in Western Hudson Bay
… 6. The second model is a system of continuous delay differential equations with time-dependent parameters, also influenced by increasing temperatures. The positivity of solutions is found, dependent on sufficient initial conditions. Numerical simulations predicted a threshold value for the …
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A Numerical Study of a Delay Differential Equation Model for Breast Cancer
… of certain drug therapies on the cancer. We use delay differential equations to model the interaction of breast cancer cells with the immune system. The new model is constructed by combining two previous models. The first model accounts for different cell cycles and includes terms to evaluate …
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Robust numerical methods to solve differential equations arising in cancer modeling
… numerical methods for nonlinear, first order delay differential equations, second order non-linear time-dependent parabolic partial (integro) differential problems and optimal control problems arising in cancer modeling. The development of cancer modeling is necessitated by the lack of …
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Stability Analysis of Time Delay Systems Using Spectral Element Method
… study the response and the stability of various delay differential equations (DDEs). The development of these new analysis techniques is motivated by the existence of delays in the governing equations of many physical systems such as turning and milling processes. </p><p>Delay differential …
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Wavelets operational methods for fractional differential equations and systems of fractional differential equations
… method to solve some singular second order differential equations of Emden-Fowler type, a class of generalized Pantograph equations and Delay differential systems. A new operational matrix of fractional order derivative and integration based on this polynomial was also developed and used …
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Spectral Solution Method for Distributed Delay Stochastic Differential Equations
Stochastic delay differential equations naturally arise in models of complex natural phenomena, yet continue to resist efforts to find analytical solutions to them: general solutions are limited to linear systems with additive noise and a single delayed term. In this work we solve the case of …
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Modeling the Impact Of Environmental Factors, Diapause and Control Strategies on Tick and Tick-Borne Disease Dynamics
… tools including dynamical systems, ordinary and delay differential equations, basic reproduction numbers and Hopf bifurcation theory. For this purpose, we produce three different models to study the effect of physiological features such as diapause, control strategies and the effect of …
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A Dynamical Nephrovascular Model of Renal Autoregulation
… is formulated with a large number of ordinary differential equations that represent the intracellular processes of arteriolar smooth muscles, coupled with a number of partial differential equations, mainly of the advection-diffusion-reaction type, that represent blood flow, glomerular …
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Reduced Order Controllers for Distributed Parameter Systems
… This includes problems governed by partial differential equations (PDEs) and delay differential equations. In order to numerically implement a controller for a physical system we often first approximate the PDE and the PDE controller using some finite dimensional scheme. However, control …
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MODELING THE DYNAMICS OF INFECTIOUS DISEASES WITH Latency IN SPATIALLY HETEROGENEOUS Environments
… structure. The model is given by a system of delay differential equations (DDEs). It is a generalization of the classical Kermack-McKendrick SIR model, and it preserves some properties that the Kermack-McKendrick model processes. We show that the ratio of final sizes in two patches is fully …
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