Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Humphries, Antony R."'
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. There are two monotone nonlinearities in the model: one describes the
Externí odkaz:
http://arxiv.org/abs/2410.13092
Publikováno v:
Journal of Computational Dynamics, 9 (2022), 421-450
Numerical bifurcation analysis, and in particular two-parameter continuation, is used in consort with numerical simulation to reveal complicated dynamics in the Mackey-Glass equation for moderate values of the delay close to the onset of chaos. In pa
Externí odkaz:
http://arxiv.org/abs/2203.00181
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 introduces nonlinearity into an otherwise linear system. We investigate the en
Externí odkaz:
http://arxiv.org/abs/2110.01850
Publikováno v:
J. Math. Biol. 84, 2 (2022)
Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we study Goodwin models of both inducible and repressible operons with stat
Externí odkaz:
http://arxiv.org/abs/2106.06628
Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic Gamma distributed DDEs are not currently available. Accordingly, modellers often resort to approx
Externí odkaz:
http://arxiv.org/abs/2104.03873
Publikováno v:
Mathematical Biosciences and Engineering, 2019, 16(5): 5419-5450
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 the resulting delay differential equation preserves non-negativity of
Externí odkaz:
http://arxiv.org/abs/1811.05930
Publikováno v:
Journal on Applied Dynamical Systems, 18 (2019), 808-852
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 marrow. One parameter continuation reveals that with a delay of just a f
Externí odkaz:
http://arxiv.org/abs/1712.08308
Autor:
De Souza, Daniel Camara, Craig, Morgan, Cassidy, Tyler, Li, Jun, Nekka, Fahima, Belair, Jacques, Humphries, Antony R
Publikováno v:
Journal of Pharmacokinetics and Pharmacodynamics, 45 (2018), 59-77
We compare and contrast the transit compartment ordinary differential equation modelling approach with distributed and discrete delay differential equation models. We focus on Quartino's extension to the Friberg transit compartment model of myelosupp
Externí odkaz:
http://arxiv.org/abs/1705.08396
Autor:
Langlois, Gabriel P., Craig, Morgan, Humphries, Antony R., Mackey, Michael C., Mahaffy, Joseph M., Bélair, Jacques, Moulin, Thibault, Sinclair, Sean R., Wang, Liangliang
Publikováno v:
Journal of Mathematical Biology volume 75, pages 1411-1462 (2017)
We develop a comprehensive mathematical model of platelet, megakaryocyte, and thrombopoietin dynamics in humans. We show that there is a single stationary solution that can undergo a Hopf bifurcation, and use this information to investigate both norm
Externí odkaz:
http://arxiv.org/abs/1608.02806