Submitted

• P. Carter, A. Doelman, A. Iuorio F. Veerman (2023), Travelling pulses on three spatial scales in a Klausmeier-type vegetation-autotoxicity model, submitted, pdf file.
• S. Banerjee, M. Baudena, P. Carter, R.Bastiaansen, A. Doelman, M. Rietkerk, (2023), Rethinking tipping points in spatial ecosystems, submitted, pdf file.

Publications

• E. Byrnes, P. Carter, A. Doelman, L. Liu (2023), Large amplitude radially symmetric spots and gaps in a dryland ecosystem model, J. Nonl. Sc., 33(6) 107.
• P. Carter, A. Doelman, K. Lilly, E. Obermayer, S. Rao (2023), Criteria for the (in)stability of planar interfaces in singularly perturbed 2-component reaction-diffusion equations, Physica D 444 133596.
• K. Siteur, Q.-X.Liu, V. Rottschäfer, T. van der Heide, M. Rietkerk, A. Doelman, C. Boström, J. van de Koppel (2023), Phase-separation physics underlies new theory for the resilience of patchy ecosystems, Proc. Nat. Acad. Sc. U.S.A. 120(2) e2202683120.
• A. Doelman (2022), Slow localized patterns in singularly perturbed 2-component reaction-diffusion equations, Nonlinearity 35 3487–3559.
• M. Rietkerk, R.Bastiaansen, S. Banerjee, J. van de Koppel, M. Baudena, A. Doelman (2021), Evasion of tipping in complex systems through spatial pattern formation, Science 374, eabj0359.
• Y. Chen, A. Doelman, K. Promislow, F. Veerman (2020), Robust stability of multicomponent membranes: the role of glycolipids, Arch. Rat. Mech. An. 238(3) 1521-1557.
• O. Jaïbi, A. Doelman, M. Chirilus-Bruckner, E. Meron (2020), The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation, Physica D 412 132637.
• R. Bastiaansen, A. Doelman, F. van Langevelde, V. Rottschäfer (2020), Modelling honey bee colonies in winter using a Keller-Segel model with a sign-changing chemotactic coefficient, SIAM J. Appl. Math. 80 (2) 839-863.
• R. Bastiaansen, A. Doelman, M.B. Eppinga, M. Rietkerk (2020), The effect of climate change on the resilience of ecosystems with adaptive spatial pattern formation, Ecology Letters 23 414-429.
• R. Bastiaansen, M. Chirilus-Bruckner, A. Doelman (2020), Pulse solutions for an extended Klausmeier model with spatially varying coefficients, SIAM J. Appl. Dyn. Syst. 19(1) 1-57.
• R. Bastiaansen, P. Carter, A. Doelman (2019), Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems, Nonlinearity 32 (8) 2759-2814.
• E. Siero, K. Siteur, A. Doelman, J. van de Koppel, M. Rietkerk, M.B. Eppinga (2019), Grazing away the resilience of patterned ecosystems, The American Naturalist 193(3) 472-480.
• R. Bastiaansen, A. Doelman (2019), The dynamics of disappearing pulses in a singularly perturbed reaction-diffusion system with parameters that vary in time and space, Physica D 388 45–72.
• P. Carter, A. Doelman (2018), Traveling stripes in the Klausmeier model of vegetation pattern formation, SIAM J. Appl. Math. 78(6) 3213-3237.
• R. Bastiaansen, O. Jaïbi, V. Deblauwe, M.B. Eppinga, K. Siteur, E. Siero, S. Mermoz, A. Bouvet, A. Doelman, M. Rietkerk (2018), Multistability of model and real dryland ecosystems through spatial self-organization, Proc. Nat. Acad. Sc. U.S.A. 115(44) 11256-11261.
• A. Doelman, J. Rademacher, B. de Rijk, F. Veerman (2018), Destabilization mechanisms of periodic pulse patterns near a homoclinic limit, SIAM J. Appl. Dyn. Syst. 17(2) 1833–1890.
• A. Doelman, P.J.A. van Heijster, J. Shen (2018), Pulse dynamics in reaction-diffusion equations with strong spatially localised impurities, Philos. Trans. Roy. Soc. A 376(2117) 20170183.
• H.T. van der Scheer, A. Doelman (2017), Synapse fits neuron: joint reduction by model inversion, Biological Cybernetics, 111(3) 309–334.
• L. Sewalt, A. Doelman (2017), Spatially periodic multi-pulse patterns in a generalized Klausmeier–Gray–Scott model, SIAM J. Appl. Dyn. Syst., 16(2) 1113–1163.
• K. Siteur, M.B. Eppinga, A. Doelman, E. Siero, M. Rietkerk (2016), Ecosystems off track: rate-induced critical transitions in ecological models, Oikos 125 1689–1699.
• A. Doelman, P.J.A. van Heijster, F. Xie (2016), A geometric approach to stationary defect solutions in one space dimension, SIAM J. Appl. Dyn. Syst. 15(2) 655-712.
• B. de Rijk, A. Doelman, J. Rademacher (2016), Spectra and stability of spatially periodic pulse patterns: Evans function factorization via Riccati transformation, SIAM J. Math. An. 48(1) 61–121.
• A. Doelman, F. Veerman (2015), An explicit theory for pulses in two component, singularly perturbed, reaction-diffusion equations, J. Dyn. Diff. Eq. 27(3-4) 555–595.
• E. Siero, A. Doelman, M.B. Eppinga, J. Rademacher, M. Rietkerk, K. Siteur (2015), Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes, Chaos 25(3) 036411.
• A. Doelman, L. Sewalt, A. Zagaris (2015), The effect of slow spatial processes on emerging spatiotemporal patterns, Chaos 25(3) 036408.
• L. Sewalt, A. Doelman, H. Meijer, V. Rottschäfer, A. Zagaris (2015), Tracking pattern evolution through extended center manifold reduction and singular perturbations, Physica D 298 48-67.
• M. Chirilus-Bruckner, A. Doelman, P.J.A. van Heijster, J. Rademacher (2015), Butterfly catastrophe for fronts in a three-component reaction-diffusion system, J. Nonl. Sc. 25 (1) 87–129.
• A. Doelman, G. Hayrapetyan, K. Promislow, B. Wetton (2014), Meander and pearling of single-curvature bilayer interfaces in the functionalized Cahn-Hilliard equation, SIAM J. Math. An. 46(6) 3640–3677.
• K. Siteur, E. Siero, M.B. Eppinga, J. Rademacher, A. Doelman, M. Rietkerk (2014), Beyond Turing: The response of patterned ecosystems to environmental change, Ecological Complexity 20 81–96.
• T. Bellsky, A. Doelman, T.J. Kaper, K. Promislow (2013), Adiabatic stability under semi-strong interactions: the weakly damped regime, Indiana Univ. Math. J. 62 (6) 1809–1859.
• Q.-X.Liu, A. Doelman, V. Rottschäfer, M. de Jager, P. M. J. Herman, M. Rietkerk, J. van de Koppel (2013), Phase separation explains a new class of self-organized spatial patterns in ecological systems, Proc. Nat. Acad. Sc. U.S.A. 110(29) 11905-11910.
• F. Veerman, A. Doelman (2013), Pulses in a Gierer-Meinhardt equation with a slow nonlinearity, SIAM J. Appl. Dyn. Syst. 12(1) 28-60.
• M. Holzer, A. Doelman, T.J. Kaper (2013), Existence and stability of traveling pulses in a reaction-diffusion-mechanics system, J. Nonl. Sc. 23(1) 129-177.
• C.J.K. Knight, G. Derks, A. Doelman, H. Susanto (2013) Stability of stationary fronts in a non-linear wave equation with spatial inhomogeneity, J. Differential Equations 254(2) 408-468.
• S. van der Stelt, A. Doelman, G.M. Hek , J. Rademacher (2013), Rise and fall of periodic patterns for a generalized Klausmeier-Gray-Scott model, J. Nonl. Sc. 23(1) 39-95.
• G. Derks, A. Doelman, C.J.K. Knight, H. Susanto (2012) Pinned fluxons in a Josephson junction with a finite-length inhomogeneity, Eur. J. Appl. Math. 23 201–244.
• A. Doelman, J. Rademacher, S. van der Stelt (2012) Hopf dances near the tips of Busse balloons, Discr. Cont. Dyn. Syst. (S) 5(1) 61-92.
• A. Zagaris, A. Doelman (2011) Emergence of steady and oscillatory localized structures in a phytoplankton-nutrient model, Nonlinearity 24 3437–3486.
• P.J.A. van Heijster, A. Doelman, T.J. Kaper, Y. Nishiura, K.-I. Ueda (2011) Pinned fronts in heterogeneous media of jump type, Nonlinearity 24 127-157.
• P.J.A. van Heijster, A. Doelman, T.J. Kaper, K. Promislow (2010) Front interactions in a three-component system, SIAM J. Appl. Dyn. Syst. 9 (2) 292-332.
• A. Doelman, B. Sandstede , A. Scheel , G. Schneider (2009) The dynamics of modulated wave trains, Memoirs of the AMS 199 (934).
• A. Zagaris , A. Doelman, N. N. Pham Thi, B. Sommeijer (2009) Blooming in a non-local, coupled phytoplankton-nutrient model, SIAM J. Appl. Math., 69 (4) 1174-1204.
• A. Doelman, P.J.A. van Heijster , T.J. Kaper (2009) Pulse dynamics in a three-component system: existence analysis, J. Dyn. Diff. Eq., 21 (1) 73-115.
• P.J.A. van Heijster , A. Doelman, T.J. Kaper (2008) Pulse dynamics in a three-component system: stability and bifurcations, Physica D, 237 (24) 3335-3368.
• A. Doelman, T.J. Kaper , K. Promislow (2007) Nonlinear asymptotic stability of the semi-strong pulse dynamics in a regularized Gierer-Meinhardt model, SIAM J. Math. An., 38 (6) 1760-1787.
• G. Derks , A. Doelman, S.A. van Gils , H. Susanto (2007) Stability analysis of $\pi$-kinks in a $0-\pi$ Josephson junction, SIAM J. Appl. Dyn. Syst., 6 (1) 99 - 141.
• A. Doelman, G.M. Hek , N.J.M. Valkhoff (2007) Algebraically decaying pulses in a Ginzburg-Landau system with a neutrally stable mode, Nonlinearity , 20 357 - 389.
• A. Doelman, T.J. Kaper , L.A. Peletier (2006) Homoclinic bifurcations at the onset of pulse self-replication, J. Differential Equations 231 359 - 423.
• M.A. Beck , A. Doelman, T.J. Kaper (2006) A geometric construction of traveling waves in a bioremediation model, J. Nonl. Sc. 16 (4) 329 - 349.
• H. van der Ploeg , A. Doelman (2005) Stability of spatially periodic pulse patterns in a class of singularly perturbed reaction-diffusion equations, Indiana Univ. Math. J. 54 (5) 1219 - 1301.
• G. M. Terra , A. Doelman, L.R.M. Maas (2004) Weakly nonlinear cubic interactions in coastal resonance, J. Fluid Mech. 520 93 - 134.
• H. Susanto , S.A. van Gils , A. Doelman, G. Derks (2004) Analysis of the stability of Josephson vortices at tricrystal boundaries: a 3 phi_0/2 case, Phys. Rev. B 69 212503.
• A. Doelman, G.M. Hek , N.J.M. Valkhoff (2004) Stabilization by slow diffusion in a real Ginzburg-Landau system, J. Nonl. Sc. 14 237 - 278.
• A. Doelman, D. Iron , Y. Nishiura (2004) Destabilization of fronts in a class of bi-stable systems, SIAM J. Math. An. 35 (6) 1420 - 1450.
• G. Derks , A. Doelman, S.A. van Gils , T.P.P. Visser (2003) Travelling waves in a singularly perturbed sine-Gordon equation, Physica D 180 (1-2) 40 - 70.
• A. Doelman, T.J. Kaper (2003) Semi-strong pulse interactions in a class of coupled reaction-diffusion equations, SIAM J. Appl. Dyn. Syst. 2 (1) 53 - 96.
• A. Doelman, B. Sandstede , A. Scheel , G. Schneider (2003) Propagation of hexagonal patterns near onset, Eur. J. Appl. Math. 14 85 - 110.
• A. Doelman, H. van der Ploeg (2002) Homoclinic stripe patterns, SIAM J. Appl. Dyn. Syst. 1 (1) 65 - 104.
• A. Doelman, A.F. Koenderink, L.R.M. Maas (2002) Quasi-periodically forced nonlinear Helmholtz oscillators, Physica D 164 (1-2) 1 - 27.
• L.R.M. Maas , A. Doelman (2002) Chaotic tides, J. Phys. Oceanogr. 32 (3) 870 - 890.
• A. Doelman, R. A. Gardner , T.J. Kaper (2002) A stability index analysis of 1-D patterns of the Gray-Scott model, Memoirs of the AMS 155 (737).
• A. Doelman, T.J. Kaper , H. van der Ploeg (2001) Spatially periodic and aperiodic multi-pulse patterns in the one-dimensional Gierer-Meinhardt equation, Meth. Appl. Anal. 8 (2) 387 - 414.
• A. Doelman, R. A. Gardner , T.J. Kaper (2001) Large stable pulse solutions in reaction-diffusion equations, Indiana Univ. Math. J. 50 (1) 443 - 507.
• A. Doelman, W. Eckhaus, T.J. Kaper (2001) Slowly-modulated two-pulse solutions in the Gray-Scott model II: geometric theory, bifurcations and splitting dynamics, SIAM J. Appl. Math. , 61 (6) 2036 - 2062.
• A. Doelman, W. Eckhaus, T.J. Kaper (2000) Slowly-modulated two-pulse solutions in the Gray-Scott model I: asymptotic construction and stability, SIAM J. Appl. Math. 61 (3) 1080 - 1102.
• D.S. Morgan , A. Doelman, T.J. Kaper (2000) Stationary periodic patterns in the 1D Gray-Scott model, Meth. Appl. Anal. 7 (1) 105-150.
• A. Doelman, G.M. Hek (2000) Homoclinic saddle-node bifurcations in singularly perturbed systems, J. Dyn. Diff. Eq. 12 (1) 169-216.
• G.M. Hek , A. Doelman, P. Holmes (1998) Homoclinic saddle-node bifurcations and subshifts in a three-dimensional flow, Arch. Rat. Mech. An. 145 291-329.
• R. Schielen, A. Doelman (1998) Modulation equations for spatially periodic systems: derivation and solutions, SIAM J. Appl. Math. 58 (6) 1901-1930.
• A. Doelman, R. A. Gardner , T.J. Kaper (1998) Stability analysis of singular patterns in the 1-D Gray-Scott model: A matched asymptotics approach, Physica D 122 1-36.
• V. Rottschäfer , A. Doelman (1998) On the transition of the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation, Physica D 118 261-292.
• A. Doelman, V. Rottschäfer (1997) Singularly perturbed and non-local modulation equations for systems with interacting instability mechanisms, J. Nonl. Sc. 7 371-409.
• A. Doelman, T.J. Kaper , P.A. Zegeling (1997) Pattern formation in the 1-D Gray-Scott model, Nonlinearity 10 523-563.
• A. Doelman (1996) Breaking the hidden symmetry in the Ginzburg-Landau equation Physica D 97 398-428.
• P. Takac , P. Bollerman, A. Doelman, A. van Harten , E.S. Titi (1996) Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg-Landau equation, SIAM J. Math. An. 27 (2) 424 - 448.
• A. Doelman, P. Holmes (1996) Errata: Homoclinic explosions and implosions, Phil. Trans. Roy. Soc. Lond. A 354 1837-1839.
• A. Doelman, P. Holmes (1996) Homoclinic explosions and implosions, Phil. Trans. Roy. Soc. Lond. A 354 845-893.
• A. Doelman, R. A. Gardner , C.K.R.T. Jones (1995) Instability of quasiperiodic solutions of the Ginzburg-Landau equation Proc. Roy. Soc. Edinb. 125A 501-517.
• A. Doelman, F. Verhulst (1994) Bifurcations of strongly nonlinear self-exited oscillations Math. Meth. Appl. Sc. 17 189-207.
• A. Doelman, E.S. Titi (1993) Regularity of solutions and the convergence of the Galerkin method in the Ginzburg-Landau equation Numer. Funct. Anal. and Opt. 14 299-321.
• R. Schielen, A. Doelman, H.E. de Swart (1993) On the nonlinear dynamics of free bars in straight channels J. Fluid Mech. 252 325-356.
• A. Doelman (1993) Traveling waves in the complex Ginzburg-Landau equation J. Nonl. Sc. 3 225-266.
• A. Doelman, W. Eckhaus (1991) Periodic and quasi-periodic solutions of degenerate modulation equations, Physica D 53 249-266.
• A. Doelman (1991) Finite dimensional models of the Ginzburg-Landau equation, Nonlinearity 4 231-250.
• A. Doelman (1989) Slow time-periodic solutions of the Ginzburg-Landau equation, Physica D 40 156-172.

Books

• A. Doelman, A. van Harten (eds.) (1995) Nonlinear Dynamics and Pattern Formation in the Natural Environment , Longman, UK; Pitman Research Notes in Mathematics 335 .

Contributions to Books

• A. Doelman (2019), Pattern formation in reaction-diffusion systems - an explicit approach, pp. 129-182 in Complexity Science (M. Peletier, R. van Santen, E. Steur (eds.)), World Scientific, pdf file.
• A. Doelman, P. Holmes (1995) On the creation of multi-pulse traveling waves by global bifurcations, pp. 201-208 in Structure and Dynamics of Nonlinear Waves in Fluids (A. Mielke & K. Kirchgässner eds.), World Scientific, Singapore etc. Advanced Series in Nonlinear Dynamics 7.
• A. Doelman, W. Eckhaus, R. Kuske, R. Schielen (1995) Pattern formation in systems on spatially periodic domains pp. 85-105 in Nonlinear Dynamics and Pattern Formation in the Natural Environment (A. Doelman, A. van Harten (eds.)), Longman, UK; Pitman Research Notes in Mathematics 335 .
• A. Doelman, E.S. Titi (1993) Exponential convergence of the Galerkin approximation for the Ginzburg-Landau equation pp 241-252 in Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, (H.G. Kaper, M. Garbey eds.), Kluwer Academic Publishers, Dordrecht.
• A. Doelman, J. Grasman (1988) Low order spectral methods in hydrodynamics, pp 86-97 in Trends in Applications of Mathematics to Mechanics , (J.F. Besseling, W. Eckhaus eds.), Springer-Verlag, Berlin etc.

Contributions to Conference Proceedings

• J. Hazewinkel , P. van Breevoort, A. Doelman, L.R.M. Maas , S.B. Dalziel (2007) Equilibrium spectrum for internal wave attractors in a trapezoidal basin, in Proceedings of the 5th International Symposium on Environmental Hydraulics (D. Boyer & O. Alexandrova eds.), Arizona State University/United States Army Research Office.
• G.M. Hek, N. Valkhoff, A. Doelman (2005) Stabilization of pulses by competing instability mechanisms, pp 2353-2361 in Proceedings ENOC-2005, Eindhoven, Netherlands.
• A. Doelman, D. Iron, Y. Nishiura (2005) Edge bifurcations in singularly perturbed reaction-diffusion equations: a case study, pp 783-788 in EQUADIFF03 International Conference on Differential Equations, (F. Dumortier, H. Broer, J. Mahwin, A. Vanderbauwhede, S. Verduyn Lunel eds.), World Scientific, Singapore etc.
• A. Doelman (2002) Stabilization of pulses by diffusion, contribution to the Biennial Report 2000-2001 of the Stieltjes Institute for Mathematics, postscript file.
• P. Holmes, A. Doelman, G.M. Hek, G. Domokos (2001) Homoclinic orbits and chaos in three- and four-dimensional flows, paper for Royal Society Discussion Meeting on Topological Methods in the Physical Sciences , London, Nov 15-16, 2000, Phil. Trans. Roy. Soc. Lond. A 359 1429-1438.
• A. Doelman, W. Eckhaus, T.J. Kaper (2000) A note on two pulse solutions in the $1$-D Gray-Scott model, pp 775-780 in EQUADIFF99, International Conference on Differential Equations 2 Vol., (B. Fiedler, K. Gröger, J. Sprekels eds.), World Scientific, Singapore etc.
• A. Doelman, R.A. Gardner, T.J. Kaper (2000) The stability of large pulse solutions in the generalized Gierer-Meinhardt equation, pp 781-786 in EQUADIFF99, International Conference on Differential Equations 2 Vol., (B. Fiedler, K. Gröger, J. Sprekels eds.), World Scientific, Singapore etc.
• A. Doelman, V. Rottschafer (1998) Multi-bump patterns near a co-dimension 2 point, Proc. Asymptotics in Nonlinear Diffusive Systems, Sendai, Japan, Tohoku Math. Pub., 8 43-54.
• A. Doelman (1993) Travelling, non-periodic patterns in nonlinear stability problems Proc. Fourth European Turbulence Conference, Delft, the Netherlands 1992 (F.T.M. Nieuwstadt ed.), Appl. Sc. Res. 51 37-42.
• A. Doelman, W. Eckhaus (1991) Quasi-periodic and homoclinic solutions of modulation equations, Proc. IUTAM-Symp. on Nonlinear Hydrodynamic Stability and Transition, Sophia-Antipolis France 1990 (G. Iooss ed.), Europ. J. Mech. B/Fluids 10 131-136.

Publications in Dutch

• A. Doelman, Dynamische systemen, patroonvorming en het ontstaan van woestijnen, Natuurkundige Voordrachten 2019-2020, Nieuwe Reeks 98 51-60 (2020).
• A. Doelman, M. Eppinga, G. M. Hek, J. Rademacher, M. Rietkerk, E. Siero, K. Siteur (2013) Klimaatsverandering, verwoestijng en biljart, Eureka! (Leiden) 10(41) 21-24, and Nieuw Archief van de Wiskunde 5/14(3) 200-204.
• A. Doelman, V. Rottschäfer, L. Sewalt, H. E. de Swart, A. Zagaris, J. Zijlstra (2013) De complexe dynamica van fytoplankton, Nieuw Archief van de Wiskunde 5/14(3) 190-194.
• A. Doelman (2007) De dynamica van patronen: wiskunde en woestijnen, Vakantiecursus 2007 Wiskunde in Beweging, CWI syllabus 57 27-45.
• A. Doelman (2003) Het begrip dimensie: theorie en experiment, Vakantiecursus 2001 Experimentele wiskunde, CWI syllabus 49 17-38, and Nieuw Archief van de Wiskunde 5/4 (2) 151-160.
• A. Doelman, H. Duistermaat, J. Grasman, A. van Harten (2001) In Memorian Wiktor Eckhaus, Nieuw Archief van de Wiskunde 5/2 (2) 18-20 (2001), and ITW Nieuws 11 (1) 10-13.
• A. Doelman (2000), Patronen en Golven , rede uitgesproken bij de aanvaarding van het ambt van hoogleraar in de Wiskunde, 27 oktober 1999, oratiereeks Vossiuspers AUP; also as Nieuw Archief van de Wiskunde 5/1 (1) 18-27.
• A. Doelman (1999) Toegepaste Analyse en Dynamische Systemen Nieuwsbrief KdV Inst. April 9-13.
• A. Doelman (1996) Patroonvorming in reactie-diffusie systemen De Vakidioot 2 2-6.

Thesis

• A. Doelman (1990) On the Nonlinear Evolution of Patterns - Modulation Equations and Their Solutions, Rijksuniversiteit Utrecht.