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- Numerical Analysis of Dynamical Systems, A.M. Stuart and A.R. Humphries, 685 + xxii pages, Cambridge University Press, Hardback 1996, Paperback 1998.

- Spurious Solutions of Numerical Methods for Initial Value Problems, A.R. Humphries. IMA J. Num. Anal., 13 (1993), 263-290.
- Runge-Kutta Methods for Dissipative and Gradient Dynamical Systems, A.R. Humphries and A.M. Stuart. SIAM J. Num. Anal., 31 (1994), 1452-1485.
- Model Problems in Numerical Stability Theory for Initial Value Problems, A.M. Stuart and A.R. Humphries. SIAM Review, 36 (1994), 226-257.
- The Essential Stability of Local Error Control for Dynamical Systems, A.M. Stuart and A.R. Humphries. SIAM J. Num. Anal., 32 (1995) 1940-1971.
- Adaptive Methods for semi-linear elliptic equations with
critical exponents and interior singularities, C.J. Budd and A.R. Humphries.
*Appl Numer. Math.*26 (1997) 227-240. - Weak Finite Dimensional Approximations of Semi-Linear
Elliptic PDEs With Near Critical Exponents, C.J. Budd and A.R. Humphries.
*J. Asymp. Anal. 17 (1998) 185-220.* - 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 J. Sci. Comp. 20, (1999) 1875-1904.* - Phase Space Error Control for Dynamical Systems, D.J.
Higham, A.R. Humphries and R.J. Wain,
*SIAM J. Sci. Comp. 21, (2000) 2275-2294.* - Mosaic
solutions and Entropy for Spatially Discrete Cahn-Hilliard
Equations, K.A. Abell, A.R. Humphries and E.S. Van Vleck,
*IMA J. Appl. Math. 65 (2000) 219-255.* - 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*. - 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.
*J. Comput. Appl. Math. 151 (2003), 59-84.*. - Phase Space Stability Error Control with Variable Time-stepping Runge-Kutta Methods for Dynamical Systems, A.R. Humphries and R. Vigneswaran,
*Appl. Num. Anal. Comp. Math. 1 (2004) 469-488.* - Computation of Mixed Type Functional Differential Boundary Value Problems,
K.A. Abell, C.E. Elmer, A.R. Humphries and E.S. Van Vleck.
*SIAM J. Appl. Dyn. Sys., 4 (2005) 755-781.* - Electromagnetic
two-body problem: recurrent dynamics in the presence of state-dependent delay, J. De Luca, N. Guglielmi, A.R. Humphries and A. Politi.
*J. Phys. A, 43 (2010) 205103 (22 pages)*. - Front Solutions for Bistable
Differential-Difference Equations with
Inhomogeneous Diffusion, A.R. Humphries, B.E. Moore, and E.S. van Vleck.
*SIAM J. Appl. Math, 71 (2011) 1374-1400.* - Dynamics of a Delay Differential Equation With Multiple State Dependent Delays,
A.R. Humphries, O.A. DeMasi, F.M.G. Magpantay and F. Upham.
*Disc. Cont. Dynam. Syst. series A, 32 (2012) 2701 - 2727.* - Finite Element Boundary Value Integration of
Wheeler-Feynman Electrodynamics, J. De Luca, A.R. Humphries, and S.B. Rodrigues,
*J. Comput. Appl. Math, 236 (2012), 3319-3337.* - 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,
*Celest. Mech. & Dynam. Astron., 114 (2012) 77 - 106.* - 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.* -
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 .* -
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.* -
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. doi:10.1007/s11538-016-0179-8 -
An upper bound
for the half-removal time of neutrophils from circulation,
M. Craig, A.R. Humphries and M.C.Mackey.
[Letter]
*Blood*, 128 (2016), 1989-1991. doi:10.1182/blood-2016-07-730325 - 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*, online first, 2017. - 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.

- 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.
- 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 MagalhÃ£es, C Rocha and L Sanchez, editors, Equadiff 95 Proceedings of the International Conference on Differential Equations, World Scientific, 1998.
- 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.
- Efficient accurate non-iterative breaking point
detection and computation for state-dependent delay differential equations., A. Eremin and A.R. Humphries.
12
^{th}International Conference on Numerical Analysis and Applied Mathematics: ICNAAM 2014.*AIP Conference Proceedings 1648, (2015) 150006.*

- A.R. Humphries and F.M.G. Magpantay. Lyapunov-Razumikhin techniques for state-dependent delay differential equations, 2015. arXiv:1507.00141 [math.DS]
- F.M.G. Magpantay and A.R. Humphries. Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations, 2017. arXiv:1703.08638 [math.DS]
- D. Camara de Souza, M. Craig, J. Bélair, T. Cassidy, J. Li, F. Nekka and A.R. Humphries. Transit and lifespan in neutrophil production: implications for drug intervention, 2017. arXiv:1705.08396 [q-bio.TO]

- A.R. Humphries and N. Christodoulou. Phase Space Error Control for Dynamical Systems, II. University of Sussex, Centre for Mathematical Analysis and its Applications Research Report no CMAIA00-13, 2000.
- A.R. Humphries and R.P. Wilds. Traveling wave solutions of lattice differential equations through an embedding approach, 2006.