Dr Philip Aston


Qualifications: BSc, PhD, MIMA, CMath

Phone: Work: 01483 68 2631
Room no: 37 AA 04

Further information


  • BSc Mathematics and Computer Science (First class honours), Brunel University, 1979-1983
  • PhD, supervisor Prof John Whiteman, Brunel University, 1983-1986
  • SERC-funded postdoc working with Prof John Toland and Prof Alastair Spence, University of Bath, 1986-1989
  • Department of Mathematics, University of Surrey, 1989 onwards

Further details can be found on my personal web page.

Research Interests

Bifurcation theory, symmetry, computation of Lyapunov exponents using spatial integration, the dynamics of bouncing balls, pharmacokinetics/pharmacodynamics (PKPD), non-exponential radioactive decay.

Further details can be found on my personal web page.


Journal articles

  • Aston PJ, Bristow N. (2013) 'Erratum: Alternating period-doubling cascades (Nonlinearity (2013) 26 (2553))'. Nonlinearity, 26 (9), pp. 2745-2745.
  • Aston PJ, Bristow N. (2013) 'Alternating Period-Doubling Cascades'. IOP Nonlinearity, 26, pp. 2553-2576.
  • Aston PJ, Derks G, Agoram BM, van der Graaf PH. (2013) 'A mathematical analysis of rebound in a target-mediated drug disposition model: I.Without feedback.'. J Math Biol,


    We consider the possibility of free receptor (antigen/cytokine) levels rebounding to higher than the baseline level after one or more applications of an antibody drug using a target-mediated drug disposition model. Using geometry and dynamical systems analysis, we show that rebound will occur if and only if the elimination rate of the drug-receptor product is slower than the elimination rates of the drug and of the receptor. We also analyse the magnitude of rebound through approximations and simulations and demonstrate that it increases if the drug dose increases or if the difference between the elimination rate of the drug-receptor product and the minimum of the elimination rates of the drug and of the receptor increases.

  • Aston PJ. (2013) 'Reply to the comment by Cleanthes A. Nicolaides'. EPL, 101 (4)
  • Aston PJ. (2012) 'Is radioactive decay really exponential?'. Institute of Physics Europhysics Letters, 97 (5) Article number 52001


    Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes. The decay of 14C can be calibrated over a period of 12550 years by comparing radiocarbon dates with dates obtained from dendrochronology. It is well known that this approach shows that radiocarbon dates of over 3000 years are in error, which is generally attributed to past variation in atmospheric levels of 14C. We note that predicted atmospheric variation (assuming exponential decay) does not agree with results from modelling, and that theoretical quantum mechanics does not predict exact exponential decay. We give mathematical arguments that non-exponential decay should be expected for slowly decaying isotopes and explore the consequences of non-exponential decay. We propose an experimental test of this prediction of non-exponential decay for 14C. If confirmed, a foundation stone of current dating methods will have been removed, requiring a radical reappraisal both of radioisotope dating methods and of currently predicted dates obtained using these methods.

  • Aston PJ, Derks G, Raji A, Agoram BM, van der Graaf PH. (2011) 'Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting in vivo potency.'. Elsevier J Theor Biol, England: 281 (1), pp. 113-121.


    We consider the relationship between the target affinity of a monoclonal antibody and its in vivo potency. The dynamics of the system is described mathematically by a target-mediated drug disposition model. As a measure of potency, we consider the minimum level of the free receptor following a single bolus injection of the ligand into the plasma compartment. From the differential equations, we derive two expressions for this minimum level in terms of the parameters of the problem, one of which is valid over the full range of values of the equilibrium dissociation constant K(D) and the other which is valid only for a large drug dose or for a small value of K(D). Both of these formulae show that the potency achieved by increasing the association constant k(on) can be very different from the potency achieved by decreasing the dissociation constant k(off). In particular, there is a saturation effect when decreasing k(off) where the increase in potency that can be achieved is limited, whereas there is no such effect when increasing k(on). Thus, for certain monoclonal antibodies, an increase in potency may be better achieved by increasing k(on) than by decreasing k(off).

  • Aston PJ, Milliken PM, Shail R. (2011) 'The bouncing motion of a superball between a horizontal floor and a vertical wall'. PERGAMON-ELSEVIER SCIENCE LTD INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 46 (1), pp. 204-221.
  • Aston PJ, Mir H. (2009) 'Period-doubling/symmetry-breaking mode interactions in iterated maps'. ELSEVIER SCIENCE BV PHYSICA D-NONLINEAR PHENOMENA, 238 (19), pp. 1992-2002.
  • Aston PJ, Shail R. (2007) 'The dynamics of a bouncing superball with spin'. TAYLOR & FRANCIS LTD DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 22 (3), pp. 291-322.
  • Aston PJ, Melbourne I. (2006) 'Lyapunov exponents of symmetric attractors'. IOP PUBLISHING LTD NONLINEARITY, 19 (10), pp. 2455-2466.

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