4 papers
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…
Numerical methods and hypoexponential approximations for gamma distributed delay differential equations
Tyler Cassidy, Peter Gillich, Antony R. Humphries +1
Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic Gamma distributed DDEs are…
A Recipe for State Dependent Distributed Delay Differential Equations
Tyler Cassidy, Morgan Craig, Antony R. Humphries
We use the McKendrick equation with variable ageing rate and randomly distributed maturation time to derive a state dependent distributed delay differential equation. We show that…