71 citations · 328 across the 17 of their papers we have counts for
11 papers · 1 filter
Practicalities of State-Dependent and Threshold Delay Differential Equations
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…
Seasonal Forcing Dominated Dynamics of a piecewise smooth Ghil-Zaliapin-Thompson ENSO model
Samuel Bolduc-St-Aubin, Antony R. Humphries
The Ghil-Zaliapin-Thompson (GZT) model, a scalar delay differential equation with periodic forcing and time-delayed feedback, captures key features of the El Nino-Southern Oscillat…
Dynamics of a state-dependent delay-differential equation
Tomas Gedeon, Antony R. Humphries, Michael C. Mackey +2
We present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model.…
Nonlinear effects of instantaneous and delayed state dependence in a delayed feedback loop
Antony R. Humphries, Bernd Krauskopf, Stefan Ruschel +1
We study a scalar, first-order delay differential equation (DDE) with instantaneous and state-dependent delayed feedback, which itself may be delayed. The state dependence introduc…
Operon Dynamics with State Dependent Transcription and/or Translation Delays
Tomas Gedeon, Antony R. Humphries, Michael C. Mackey +3
Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we st…
Dynamics of a Mathematical Hematopoietic Stem-Cell Population Model
Daniel C. De Souza, Antony R. Humphries
We explore the bifurcations and dynamics of a scalar differential equation with a single constant delay which models the population of human hematopoietic stem cells in the bone ma…
Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations
F. M. G. Magpantay, A. R. Humphries
We present generalised Lyapunov-Razumikhin techniques for establishing global asymptotic stability of steady-state solutions of scalar delay differential equations. When global asy…
Resonance phenomena in a scalar delay differential equation with two state-dependent delays
R. C. Calleja, A. R. Humphries, B. Krauskopf
We study a scalar DDE with two delayed feedback terms that depend linearly on the state. The associated constant-delay DDE, obtained by freezing the state dependence, is linear and…
Lyapunov-Razumikhin techniques for state-dependent delay differential equations
A. R. Humphries, F. M. G. Magpantay
We present Lyapunov stability and asymptotic stability theorems for steady state solutions of general state-dependent delay differential equations (DDEs) using Lyapunov-Razumikhin…
Periodic Solutions of a Singularly Perturbed Delay Differential Equation With Two State-Dependent Delays
A. R. Humphries, D. A. Bernucci, R. Calleja +2
Periodic orbits and associated bifurcations of singularly perturbed state-dependent delay differential equations (DDEs) are studied when the profiles of the periodic orbits contain…
Computing Invariant Manifolds and Connecting Orbits in the Circular Restricted Three Body Problem
Renato C. Calleja, Eusebius J. Doedel, Antony R. Humphries +2
We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordi…