Search Results - "Humphries, A. R."

A Mathematical Model of Granulopoiesis Incorporating the Negative Feedback Dynamics and Kinetics of G-CSF/Neutrophil Binding and Internalization by Craig, M., Humphries, A. R., Mackey, M. C.

“…We develop a physiological model of granulopoiesis which includes explicit modelling of the kinetics of the cytokine granulocyte colony-stimulating factor…”
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Periodic Solutions of a Singularly Perturbed Delay Differential Equation with Two State-Dependent Delays by Humphries, A. R., Bernucci, D. A., Calleja, R. C., Homayounfar, N., Snarski, M.

“…Periodic orbits and associated bifurcations of singularly perturbed state-dependent delay differential equations (DDEs) are studied when the profiles of the…”
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Boundary-value problem formulations for computing invariant manifolds and connecting orbits in the circular restricted three body problem by Calleja, R. C., Doedel, E. J., Humphries, A. R., Lemus-Rodríguez, A., Oldeman, E. B.

“…We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable…”
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Runge-Kutta Methods for Dissipative and Gradient Dynamical Systems by Humphries, A. R., Stuart, A. M.

“…The numerical approximation of dissipative initial value problems by fixed time-stepping Runge-Kutta methods is considered and the asymptotic features of the…”
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Model Problems in Numerical Stability Theory for Initial Value Problems by Stuart, A. M., Humphries, A. R.

“…In the past numerical stability theory for initial value problems in ordinary differential equations has been dominated by the study of problems with simple…”
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Numerical and analytical estimates of existence regions for semi-linear elliptic equations with critical Sobolev exponents in cuboid and cylindrical domains by Budd, C.J, Humphries, A.R

“…We use a variety of careful numerical and semi-analytical methods to investigate two outstanding conjectures on the solutions of the parametrised semi-linear…”
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FRONT SOLUTIONS FOR BISTABLE DIFFERENTIAL-DIFFERENCE EQUATIONS WITH INHOMOGENEOUS DIFFUSION by HUMPHRIES, A. R., MOORE, BRIAN E., VAN VLECK, ERIK S.

“…We consider a bistable differential-difference equation with inhomogeneous diffusion. Employing a piecewise linear nonlinearity, often referred to as McKean's…”
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Mosaic solutions and entropy for spatially discrete Cahn–Hilliard equations by Abell, K. A., Humphries, A. R., Van Vleck, E. S.

“…We consider arrays of scalar differential equations organized on a spatial lattice in a form analogous to the Cahn–Hilliard partial differential equation which…”
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The Essential Stability of Local Error Control for Dynamical Systems by Stuart, A. M., Humphries, A. R.

“…Although most adaptive software for initial value problems is designed with an accuracy requirement--control of the local error--it is frequently observed that…”
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Lyapunov-Razumikhin techniques for state-dependent delay differential equations by Humphries, A. R, Magpantay, F. M. G

“…Journal of Differential Equations, Volume 304, 2021, 287-325 We present Lyapunov stability and asymptotic stability theorems for steady state solutions of…”
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Lyapunov-Razumikhin techniques for state-dependent delay differential equations by Humphries, A.R., Magpantay, F.M.G.

“…We present Lyapunov stability and asymptotic stability theorems for steady state solutions of general state-dependent delay differential equations (DDEs) using…”
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Resonance phenomena in a scalar delay differential equation with two state-dependent delays by Calleja, R. C, Humphries, A. R, Krauskopf, B

“…SIAM Journal on Applied Dynamical Systems, 16 (2017), 1474-1513 We study a scalar DDE with two delayed feedback terms that depend linearly on the state. The…”
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Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations by Magpantay, F. M. G, Humphries, A. R

“…Discrete & Continuous Dynamical Systems - S, 13 (2020) 85-104 We present generalised Lyapunov-Razumikhin techniques for establishing global asymptotic…”
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Periodic Solutions of a Singularly Perturbed Delay Differential Equation With Two State-Dependent Delays by Humphries, A. R, Bernucci, D. A, Calleja, R, Homayounfar, N, Snarski, M

“…J Dyn Diff Equat (2016) 28: 1215 Periodic orbits and associated bifurcations of singularly perturbed state-dependent delay differential equations (DDEs) are…”
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Finite element boundary value integration of Wheeler–Feynman electrodynamics by De Luca, Jayme, Humphries, A.R., Rodrigues, Savio B.

“…The electromagnetic two-body problem is solved as a boundary value problem associated to an action functional. We show that the functional is Fréchet…”
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Mosaic solutions and entropy for discrete coupled phase-transition equations by Abell, K.A., Humphries, A.R., Van Vleck, E.S.

“…We consider arrays of coupled scalar differential equations organized on a spatial lattice. One component of this system is analogous to the Allen–Cahn partial…”
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Adaptive methods for semi-linear elliptic equations with critical exponents and interior singularities by Budd, C.J., Humphries, A.R.

“…We consider the effectiveness of adaptive finite element methods for finding the finite element solutions of the parametrised semi-linear elliptic equation Δ u…”
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165. The Gulf Division Ehalo Dance by Humphries, A. R.

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The essential stabililty of local error control for dynamical systems by STUART, A. M, HUMPHRIES, A. R

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The Gulf Division "Ehalo" Dance by Humphries, A R

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