Publications are all listed below by category in chronological order. Alternatively you can access my publication list via I have included links to the pdf of the paper where they are freely available and to the doi of each paper. Submitted versions of many recent papers can also be found on the arXiv or bioRχiv.
  1. Dynamical Systems and Numerical Analysis, A.M. Stuart and A.R. Humphries, 685 + xxii pages, Cambridge University Press, Hardback 1996, Paperback 1998.
  1. Numerical Analysis of Dynamical Systems, A.R. Humphries, PhD, 1993, University of Bath. [pdf]
  1. Spurious Solutions of Numerical Methods for Initial Value Problems, A.R. Humphries. IMA Journal of Numerical Analysis, 13 (1993), 263-290. [pdf]
  2. Runge-Kutta Methods for Dissipative and Gradient Dynamical Systems, A.R. Humphries and A.M. Stuart. SIAM Journal on Numerical Analysis, 31 (1994), 1452-1485. [pdf]
  3. Model Problems in Numerical Stability Theory for Initial Value Problems, A.M. Stuart and A.R. Humphries. SIAM Review, 36 (1994), 226-257. [pdf]
  4. The Essential Stability of Local Error Control for Dynamical Systems, A.M. Stuart and A.R. Humphries. SIAM Journal on Numerical Analysis, 32 (1995) 1940-1971. [pdf]
  5. Adaptive Methods for semi-linear elliptic equations with critical exponents and interior singularities, C.J. Budd and A.R. Humphries. Applied Numerical Mathematics 26 (1998) 227-240. [pdf]
  6. Weak Finite Dimensional Approximations of Semi-Linear Elliptic PDEs With Near Critical Exponents, C.J. Budd and A.R. Humphries. Asymptotic Analysis 17 (1998) 185-220. [pdf]
  7. The finite element approximation of Semi-linear Elliptic PDEs with Critical Sobolev Exponents in the cube, C.J. Budd, A.R. Humphries and A.J. Wathen. SIAM Journal on Scientific Computing 20, (1999) 1875-1904. [pdf]
  8. Phase Space Error Control for Dynamical Systems, D.J. Higham, A.R. Humphries and R.J. Wain, SIAM Journal on Scientific Computing 21, (2000) 2275-2294. [pdf]
  9. Mosaic solutions and Entropy for Spatially Discrete Cahn-Hilliard Equations, K.A. Abell, A.R. Humphries and E.S. Van Vleck, IMA Journal of Applied Mathematics 65 (2000) 219-255. [pdf]
  10. Mosaic solutions and Entropy for Spatially Discrete Coupled Phase Transition Equations, K.A. Abell, A.R. Humphries and E.S. Van Vleck, Physica D, 155 (2001), 274-310. [pdf]
  11. Numerical and analytical estimates of existence regions for Semi-linear Elliptic equations with Critical Sobolev Exponents in cuboid and cylindrical domains, C.J. Budd and A.R. Humphries. Journal of Computational and Applied Mathematics 151 (2003), 59-84. [open archive pdf]
  12. Phase Space Stability Error Control with Variable Time-stepping Runge-Kutta Methods for Dynamical Systems, A.R. Humphries and R. Vigneswaran, Applied Numerical Analysis & Computational Mathematics 1 (2004) 469-488. [pdf]
  13. Computation of Mixed Type Functional Differential Boundary Value Problems, K.A. Abell, C.E. Elmer, A.R. Humphries and E.S. Van Vleck. SIAM Journal on Applied Dynamical Systems, 4 (2005) 755-781. [pdf]
  14. Electromagnetic two-body problem: recurrent dynamics in the presence of state-dependent delay, J. De Luca, N. Guglielmi, A.R. Humphries and A. Politi. Journal of Physics A, 43 (2010) 205103 (22 pages). [Submitted pdf]
  15. Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion, A.R. Humphries, B.E. Moore, and E.S. van Vleck. SIAM Journal on Applied Mathematics, 71 (2011) 1374-1400. [pdf]
  16. Dynamics of a Delay Differential Equation With Multiple State Dependent Delays, A.R. Humphries, O.A. DeMasi, F.M.G. Magpantay and F. Upham. Discrete & Continuous Dynamical Systems - A, 32 (2012) 2701 - 2727. [pdf]
  17. Finite Element Boundary Value Integration of Wheeler-Feynman Electrodynamics, J. De Luca, A.R. Humphries, and S.B. Rodrigues, Journal of Computational and Applied Mathematics, 236 (2012), 3319-3337. [open archive pdf]
  18. Boundary-Value Problem Formulations for Computing Invariant Manifolds and Connecting Orbits in the Circular Restricted Three Body Problem, R.C. Calleja, E.J. Doedel, A.R. Humphries, A. Lemus, B.E. Oldeman, Celestial Mechanics and Dynamical Astronomy, 114 (2012) 77 - 106. [SharedIt pdf] [submitted arXiv pdf]
  19. Synchronization in ecological systems by weak dispersal coupling with time delay, E. Wall, F. Guichard and A.R. Humphries, Theoretical Ecology, 6 (2013), 405-418. [SharedIt pdf] [submitted arXiv pdf]
  20. Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: Mathematical modelling guides dose optimisation to minimise neutropenia, M. Craig, A.R. Humphries, J. Bélair, J. Li, M.C. Mackey, and F. Nekka. Journal of Theoretical Biology, 385 (2015) 77-89 . [submitted pdf]
  21. Periodic Solutions of a Singularly Perturbed Delay Differential Equation With Two State-Dependent Delays, A.R. Humphries, D.A. Bernucci, R. Calleja, N. Homayounfar and M. Snarski. Journal of Dynamics and Differential Equations, 28 (2016) 1215-1263. [SharedIt pdf] [submitted arXiv pdf]
  22. A mathematical model of granulopoiesis incorporating the negative feedback dynamics and kinetics of G-CSF/neutrophil binding and internalisation, M. Craig, A.R. Humphries and M.C. Mackey. Bulletin of Mathematical Biology, 78 (2016) 2304-2357. [SharedIt pdf] [submitted arXiv pdf]
  23. An upper bound for the half-removal time of neutrophils from circulation, M. Craig, A.R. Humphries and M.C. Mackey. Blood, 128 (2016), 1989-1991. [pdf]
  24. Normal and pathological dynamics of platelets in humans, G. Provencher Langlois, M. Craig, A.R. Humphries, M.C. Mackey, J.M. Mahaffy, J. Bélair, T. Moulin, S.R. Sinclair and L. Wang. Journal of Mathematical Biology, 75 (2017), 1411-1462. [SharedIt pdf] [submitted arXiv pdf]
  25. Resonance phenomena in a scalar delay differential equation with two state-dependent delays, R.C. Calleja, A.R. Humphries and B. Krauskopf. SIAM Journal on Applied Dynamical Systems, 16 (2017), 1474-1513. [pdf]
  26. Transit and lifespan in neutrophil production: implications for drug intervention, D. Camara de Souza, M. Craig, T. Cassidy, J. Li, F. Nekka, J. Bélair and A.R. Humphries. Journal of Pharmacokinetics and Pharmacodynamics, 45 (2018), 59-77. [SharedIt pdf] [submitted arXiv pdf]
  27. Dynamics of a Mathematical Hematopoietic Stem-Cell Population Model, D. Camara de Souza and A.R. Humphries. SIAM Journal on Applied Dynamical Systems, 18 (2019), 808-852. [pdf]
  28. Equivalences Between Age Structured Models and State Dependent Distributed Delay Differential Equations, T. Cassidy, M. Craig and A.R. Humphries. Mathematical Biosciences and Engineering, 16 (2019), 5419-5450. [open access pdf]
  29. Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations, F.M.G. Magpantay and A.R. Humphries. Discrete & Continuous Dynamical Systems - S, 13 (2020) 85-104. [open access pdf]
  30. A mathematical model of viral oncology as an immuno-oncology instigator, T. Cassidy and A.R. Humphries. Mathematical Medicine and Biology, 37 (2020), 117-151. [pdf] [submitted bioRxiv pdf]
  31. Characterizing chemotherapy-induced neutropenia and monocytopenia through mathematical modelling, T. Cassidy, A.R. Humphries, M. Craig and M.C. Mackey. Bulletin of Mathematical Biology, 82 (2020), Article 104, 26 pages. [submitted bioRxiv pdf] [SharedIt pdf]
  32. Lyapunov-Razumikhin techniques for state-dependent delay differential equations, A.R. Humphries and F.M.G. Magpantay. Journal of Differential Equations, 304 (2021), 287-325. [submitted arXiv pdf]
  33. Operon Dynamics with State Dependent Transcription and/or Translation Delays, T. Gedeon, A.R. Humphries, M.C. Mackey, H.-O. Walther and Z. Wang. Journal of Mathematical Biology, 84 (2022), Article 2, 74 pages. [SharedIt pdf] [submitted arXiv pdf]
  34. Bistability, Bifurcations and Chaos in the Mackey-Glass Equation, V. Duruisseaux and A.R. Humphries. Journal of Computational Dynamics, 9 (2022), 421-450. [submitted arXiv pdf]
  35. Nonlinear effects of instantaneous and delayed state dependence in a delayed feedback loop, A.R. Humphries, B. Krauskopf, S. Ruschel, and J. Sieber. Discrete & Continuous Dynamical Systems - B, 27 (2022), 7245-7273. [submitted arXiv pdf]
  36. Numerical Methods and Hypoexponential Approximations for Gamma Distributed Delay Differential Equations, T. Cassidy, P. Gillich, A.R. Humphries, and C.H. van Dorp. IMA Journal on Applied Mathematics, 87, (2022), 1043-1089. [submitted arXiv pdf]
  1. Approximation of Dissipative Partial Differential Equations over Long Time Intervals, 180-207 in Numerical Analysis, 1993, Proceedings of the 15th Dundee Numerical Analysis Conference, June-July 1993", (eds. DF Griffiths and GA Watson), Longman, 1994, AR Humphries, DA Jones and A.M. Stuart.
  2. Finite Element Method Solutions for Semi-linear Elliptic PDEs with Critical Sobolev Exponents on Non-spherical 3D Domains, A.R. Humphries, C.J. Budd and Wathen, 418--425 in LT Magalhães, C Rocha and L Sanchez, editors, Equadiff 95 Proceedings of the International Conference on Differential Equations, World Scientific, 1998.
  3. Deterministic and Random Dynamical Systems: Theory and Numerics, A.R. Humphries and A.M. Stuart. In Modern Methods in Scientific Computing and Applications, NATO Science Series II, volume 75, Kluwer Academic Publishers, 2002.
  4. Efficient accurate non-iterative breaking point detection and computation for state-dependent delay differential equations., A. Eremin and A.R. Humphries. 12th International Conference on Numerical Analysis and Applied Mathematics: ICNAAM 2014. AIP Conference Proceedings 1648, (2015) 150006.
  5. Some issues with the numerical treatment of delay differential equations., A.S. Eremin, A.R. Humphries and A.A. Lobaskin. International Conference on Numerical Analysis and Applied Mathematics: ICNAAM 2019. AIP Conference Proceedings 2293, (2020) 100003.
  6. Numerical Methods for Delay Differential Equations with Threshold State-Dependent Delay. Z. Wang and A.R. Humphries. Proceedings of 17th IFAC Workshop on Time Delay Systems TDS 2022, Montreal, Canada, September 27-30, 2022. IFAC PapersOnLine 55-36 (2022) 163–168.
  1. Dynamics of a state-dependent delay-differential equation, T. Gedeon, A.R. Humphries, M.C. Mackey, H.-O. Walther and Z. Wang, arXiv:2410.13092 [math.DS], 96 pages, 2024. [submitted arXiv pdf]
  1. Phase Space Error Control for Dynamical Systems, II, 2000. A.R. Humphries and N. Christodoulou. University of Sussex, Centre for Mathematical Analysis and its Applications Research Report no CMAIA00-13.
  2. Traveling wave solutions of lattice differential equations through an embedding approach, 2006. A.R. Humphries and R.P. Wilds.