Gianne Derks

• Contact Details
• Publications
• Research Interests
• Teaching

Preprints and Publications Gianne Derks

Preprints

• C. Brown, G Derks, P. van Heijster, and D.J.B. Lloyd, "Analysing transitions from a Turing instability to large periodic patterns in a reaction-diffusion system". Submitted. ArXiV link.
• T.J. Bridges and G. Derks, "Dimension breaking of nonlinear elliptic PDEs: satisfying the spectral condition geometrically". Submitted. href="http://www.maths.surrey.ac.uk/personal/st/G.Derks/Publications/dim_breaking.pdf">Pdf preprint.

Published papers

• A. Nasim, J. Yates, G. Derks, C. Dunlop, "A spatially resolved mechanistic growth law for cancer drug development predicting tumour growing fractions", Cancer Research Communications crc-22-0032, 2022. Link to paper (Open Access)
• G. Derks, P.A. Glendinning, and A.C. Skeldon,"Creation of discontinuities in circle maps", Proc. R. Soc. A , 477: 20200872, 2021.
  Link to paper (Open Access), ArXiV link.
• J. Brooks, G. Derks, and D.J.B. Lloyd, "Existence of stationary fronts in a system of two coupled wave equations with spatial inhomogeneity". Nonlinearity, 32, pp 4147-4187, 2019.
  Link to paper (Open Access_, ArXiV link.
• L. Cucurull-Sanchez, M. Chappell, V. Chelliah, A. Cheung, G. Derks, M. Penney, A. Phipps, R. Malik-Sheriff, J. Timmis, M. Tindall, P. van der Graaf, P. Vicini, and J. Yates, "Best practices to maximise the use and re-use of QSP models: Recommendations from the UK QSP Network". CPT: Pharmacometrics & Systems Pharmacology, 2019.
  Link to paper
• M.P. Bailey, G. Derks, and A.C. Skeldon, "Circle maps with gaps: understanding the dynamics of the two process model for sleep-wake regulation". Eur. J. Appl. Math., 29 pp 845-868 2018.
  Link to paper
• A.C. Skeldon and G. Derks, "Nonsmooth maps and the fast-slow dynamics of sleep-wake regulation: Part 1", in: Research Perspectives CRM Barcelona (Trends in Mathematics series); Colombo A., Jeffrey M., Lazaro J., Olm J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics, 8, Birkhauser, pp 167-170, 2017.
  link to paper
• A.C. Skeldon, G. Derks}, V. Booth, "Nonsmooth maps and the fast-slow dynamics of sleep-wake regulation: Part 2", in: Research Perspectives CRM Barcelona (Trends in Mathematics series); Colombo A., Jeffrey M., Lazaro J., Olm J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics, 8, Birkhauser, pp 171--175, 2017.
  link to paper
• C. Gavin, P.J. Aston, G. Derks, "Extending Slow Manifolds Near a Degenerate Transcritical Intersection in Three Dimensions", in: Research Perspectives CRM Barcelona (Trends in Mathematics series); Colombo A., Jeffrey M., Lazaro J., Olm J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics, 8, Birkhauser, pp 65-70, 2017.
  DOI link
• P.J. Aston, G. Derks, B.M. Agoram, and P.H. van der Graaf, ``A Mathematical Analysis of Rebound in a Target-Mediated Drug Disposition Model. II. With feedback'', Journal of Mathematical Biology, 75 pp 33-85, 2017.
  journal link (open access); DOI link; Pdf preprint.
• J.P. Ward, J.L. Dunster, G. Derks, P. Mistry, J.D. Salazar. ``Predicting tyrosinaemia: a mathematical model of 4-hydroxyphenylpyruvate dioxygenase inhibition by nitisinone in rats'', Math. Med. Biol., 34 pp 335-390, 2017
  Pdf preprint (pre-proof).
• C.J.K. Knight, G.Derks. "A stability criterion for the non-linear wave equation with spatial inhomogeneity". Journal of Differential Equations, 259, pp 4745-4762, 2015
  DOI link, ArXiV preprint, and preprint pdf.
• A.C. Skeldon, G. Derks, and D.J. Dijk. "Modelling changes in sleep timing and duration across the lifespan: changes in circadian rhythmicity or sleep homeostasis?", Sleep Medicine Reviews, 28, pp 92-103, 2016
  Pre Author version (pre proofs) at publisher, DOI link.
• G. Derks. "Stability of Fronts in Inhomogeneous Wave Equations", Acta Applicandae Mathematicae, 137, pp 61-78, 2014. (This is a tutorial paper).
  Pdf preprint. Online-first link at Springer.
• A.C. Skeldon, D.J. Dijk, G. Derks. "Mathematical models for sleep-wake dynamics: comparison of the two process model and a mutual inhibition neuronal model", PLOS ONE, 9:e103877, 2014.
  PLOS ONE or preprints can be found at the arXiv or the University preprint server.
• P.J. Aston, G. Derks, B.M. Agoram, and P.H. van der Graaf, ``A Mathematical Analysis of Rebound in a Target-Mediated Drug Disposition Model: I. Without feedback'', Journal of Mathematical Biology, 68, pp 1453-1478, 2013.
  DOI link; Pdf preprint.
• C.J.K. Knight, G. Derks, A. Doelman, H. Susanto "Stability of stationary fronts in a non-linear wave equation with spatial inhomogeneity". Journal of Differential Equations, 254, pp. 408-468, 2013.
  DOI link; Pdf preprint.
• G. Derks, A. Doelman, C.J.K. Knight, and H. Susanto, ``Pinned fluxons in a Josephson junction with a finite length inhomogeneity''. Eur. J. Appl. Math., 23, pp. 201-244, 2012.
  DOI link; Pdf preprint; arXiv preprint.
• G. Derks and G. Gaeta, "A minimal model of DNA dynamics in interaction with RNA-Polymerase", Physica D, 240, pp. 1805-1817, 2011.
  DOI link; Pdf preprint.
• P.J. Aston, G.Derks, A. Raji, B.M. Agoram, and P.H. van der Graaf, ``Mathematical Analysis of the Pharmacokinetic-Pharmacodynamic (PKPD) Behaviour of Monoclonal Antibodies: Predicting in vivo Potency''. J. Th. Biol., 281, pp. 113-121, 2011.
  DOI link; Pdf preprint.
• G. Derks, S. Maad and B. Sandstede, "Perturbations of embedded eigenvalues for the planar bilaplacian". J. Func. Anal., 260, pp. 340-398, 2011.
  DOI link, arXiv, Pdf preprint.
• U. Ebert, F. Brau, G. Derks, W. Hundsdorfer, C.-Y. Kao, C. Li, A. Luque, B. Meulenbroek, S. Nijdam, V. Ratushnaya, L. Schäfer, S. Tanveer, "Multiple scales in streamer discharges, with an emphasis on moving boundary approximations". Nonlinearity 24, pp. C1-C26, 2011.
  DOI link (free access in 2011) and cover illustration of Nonlinearity in 2011, related to this review.
• H. Susanto and G. Derks, ``Localized mode interactions in 0-π Josephson junctions''. Phys. Rev B, 82, 132301, 2010 (4 pages).
  DOI link, PRB link, arXiv, Pdf preprint.
• G. Derks, "Existence and Uniqueness of Solutions of Initial Value Problems". In: Encyclopedia of Complexity and Systems Science, R.A. Meyers (Ed.), pp 3255-3267, 2009.
  DOI link, Springer link link, google books.
• G.Derks, "Book review: Geometric mechanics", Journal of Geometric Mechanics, pp. 267 - 270, 2009.
  DOI link
• K.B. Blyuss and G. Derks, ``Transverse intersection of invariant manifolds in perturbed multi-symplectic systems''. Dynamical Systems, 23, pp 219 - 256, 2008.
  DOI link, pdf on University preprint server, pdf preprint.
• G. Derks, U. Ebert and B. Meulenbroek. ``Laplacian instability of planar streamer ionization fronts - an example of pulled front analysis''. Journal Nonl. Science, 18, pp 551 - 590, 2008.
  And an short erratum: Journal Nonl. Science, 18, pp 591 - 592, 2008
  pdf preprint, the final publication is available at www.springerlink.com with a short erratum.
• Comment by U. Ebert and G. Derks, Phys. Rev. Lett. 101, 139501 (2008) on M. Arrayás, M.A. Fontelos, J.L. Trueba, Phys. Rev. Lett. 95, 165001 (2005). Link to journal, Surrey institutional repository, and Pdf.
• G. Derks, S. Maad and B. Sandstede. ``Perturbations of embedded eigenvalues for the bilaplacian on a cylinder''. Discrete and Continuous Dynamical Systems A, 21, pp 801-821, 2008.
  DOI link, pdf preprint.
• G. Derks, A. Doelman, S.A. van Gils, and H. Susanto, ``Stability analysis of π-kinks in a 0-π Josephson junction''. SIAM J. Applied Dynamical Systems, 6, pp 99-141, 2007.
  pdf on University preprint server, link to journal for paper, pdf preprint.
• G. Derks and G. Gottwald, ``A robust numerical method to study oscillatory instability of gap solitary waves''. SIAM J. Applied Dynamical Systems, 4, pp 140-158, 2005.
  pdf on University preprint server, link to journal for paper, pdf preprint on arXiv preprint server.
• H. Susanto, S.A. van Gils, A. Doelman, and G. Derks, `` Analysis on the stability of Josephson vortices at tricrystal boundaries: A 3φ₀/2-flux case''. Physical Review B, 69, 212503, 2004.
  link to journal for paper,pdf on University preprint server, pdf preprint.
• G. Derks, A. Doelman, S.A. van Gils and T. Visser, ``Travelling waves in a singularly perturbed sine-Gordon equation''. Physica D 180, pp 40-70, 2003.
  Link to journal for paper, pdf preprint.
• K.B. Blyuss, T.J. Bridges and G. Derks, ``Transverse instability and its long-term development for solitary waves of the (2+1)-dimensional Boussinesq equation''. Phys. Rev. E 67, 056626 (9 pages), 2003.
  pdf on University preprint server, Link to journal for paper, pdf preprint.
• T.J. Bridges and G. Derks, ``Constructing the symplectic Evans Matrix using maximally analytic individual vectors''. Roy. Soc. Edinburgh Proc. A 133, pp 505-526 (2003).
  pdf preprint.
• T.J. Bridges, G. Derks and G. Gottwald, ``Stability and instability of solitary waves of the fifth-order KDV equation: a numerical framework''. Physica D 172, pp 190-216, 2002.
  Link to journal for paper, pdf preprint.
• G.Derks and T. Ratiu, ``Unstable manifolds of relative equilibria in Hamiltonian systems with dissipation''. Nonlinearity 15, pp 531-549, 2002.
  Link to journal for paper, pdf preprint.
• T.J. Bridges and G. Derks, ``Linear instability of solitary wave solutions of the Kawahara equation and its generalizations''. SIAM J. Math. Anal. 33, pp 1356-1378, 2002.
  pdf on University preprint server, DOI, gzipped postscript preprint.
• T.J. Bridges and G. Derks, ``The symplectic Evans matrix, and the instability of solitary waves and fronts''. Arch. Rat. Mech. Anal. 156, pp 1-87, 2001.
  Link to journal for paper, pdf preprint.
• T.J. Bridges and G. Derks, ``The symplectic Evans matrix and solitary wave instability''. Conference proceedings Symmetry and Perturbation Theory 2001, editors: D. Bambusi, G. Gaeta and M. Cadoni, World Scientific, pp 32-38, 2001.
  pdf preprint.
• G. Derks, ``Families of relative equilibria in Hamiltonian systems with dissipation''. Conference proceedings Symmetry and Perturbation Theory 1998, editors: A. Degasperis and G. Gaeta, World Scientific, pp 38-58, 1999.
  pdf preprint.
• T.J. Bridges and G. Derks, ``Unstable eigenvalues and the linearisation about solitary waves and fronts with symmetry''. Proceedings of the Royal Society London, A:455, pp 2427-2469, 1999.
  pdf on University preprint server, Link to journal for paper, gzipped postscript preprint.
• T.J. Bridges and G. Derks, ``Hodge duality and the Evans function''. Physics Letters A, 251, pp 363-372, 1999.
  Link to journal for paper, gzipped postscript preprint.
• G.Derks and T. Ratiu, ``Attracting curves on families of stationary solutions in two-dimensional Navier-Stokes and reduced magnetohydrodynamics''. Proceedings of the Royal Society London, A:454, pp 1406-1444, 1998.
  pdf on University preprint server, Link to journal for paper.
• G. Derks and E. van Groesen, ``Dissipation in Hamiltonian systems: Decaying cnoidal waves''. SIAM Journ. of Math. Anal. 27, pp 1424-1447,1996.
  pdf on University preprint server, Link to journal for paper.
• G. Derks, D. Lewis and T. Ratiu, ``Approximations with curves of relative equilibria in Hamiltonian systems with dissipation''. Nonlinearity 8, pp 1087-1113, 1995.
  Link to journal for paper.
• D.H. Hepting, G. Derks, K.D. Edoh, R.D. Russell, ``Qualitative analysis of invariant tori in a dynamical system''. In G.M. Nielson and D. Silver, editors, Visualization '95 Proceedings. IEEE, IEEE Computer Society Press, Los Alamitos, California, pp 342-345, 1995.
• G. Derks and S.A. van Gils, ``On the uniqueness of traveling waves in perturbed Korteweg-de Vries equations''. Jap. Journ. of Indus. and Appl. Math. 10, pp 413-430, 1993.
• G. Derks and E. van Groesen, ``Energy propagation in dissipative systems. Part II: Centrovelocity for nonlinear wave equations''. Wave Motion 15, pp 159-172, 1992.
  Link to journal for paper.
• G. Derks and T.P. Valkering, ``Approximation in a damped Hamiltonian system by successive relative equilibria''. Jap. Journ. of Indus. and Appl. Math. 9, pp 141-161, 1992.
• G. Derks, E. van Groesen and T.P. Valkering, ``Decay of coherent structures in dissipative Hamiltonian systems''. In: Integration of theory and applications in applied mechanics. J.F. Dijksman, F.T.M. Nieuwstadt (eds.), Kluwer Academic Press, pp 329-340, 1990.
• T.P. Valkering, G. Derks and E. van Groesen, ``Modeling one degree of freedom behavior of dissipative {H}amiltonian systems with forcing''. In: Proceedings of the international conference on 'Singular behavior and nonlinear dynamics'. Proceedings 2, World Scientific, 1989.

Posters

• G.Derks, P.J Aston B.M. Agoram, P.H. Van Der Graaf. Predicting rebound for mAbs using the TMDD model. 7th Noordwijkerhout Symposium on Pharmacokinetics, Pharmacodynamics and Systems Pharmacology, Noordwijkerhout, the Netherlands, 23-25 April 2014.
  Pdf of poster.
• A. Raji, P.J. Aston, G. Derks, D.J.B. Lloyd, B.M. Agoram, P.H. Van Der Graaf. Mathematical Analysis of PKPD Behaviour of Monoclonal Antibodies: Predicting in vivo Potency and Rebound 6th International Symposium on Measurement and Kinetics of In Vivo Drug Effects. Noordwijkerhout, Netherlands, April 21-24, 2010.
  Pdf of poster.

Theses

• G. Derks, Coherent Structures in the Dynamics of Perturbed Hamiltonian Systems. PhD-thesis, University of Twente, Enschede, The Netherlands, 1992.
• G. Derks, Fractionele Integratie, Fractionele Differentiatie, Fractionele Sobolevruimten (Fractional Integration, Fractional Differentiation, Fractional Sobolev Spaces), Master's thesis, University of Technology, Eindhoven, The Netherlands, 1988 (in Dutch).