Publications of Hinke Osinga
Books Journals Book Chapters Proceedings Other Preprints

Books

	Numerical Continuation Methods for Dynamical Systems: Path following and boundary value problems B. Krauskopf, H.M. Osinga and J. Galán-Vioque (Eds.) Springer-Verlag, 2007.
	Nonlinear Dynamics and Chaos: Where do we go from here? S.J. Hogan, A.R. Champneys, B. Krauskopf, M. di Bernardo, R.E. Wilson, H.M. Osinga and M.E. Homer (Eds.) Institute of Physics Publishing, 2002.

Publications in Academic Journals

1. Global invariant manifolds near a Shilnikov homoclinic bifurcation (preprint)
   Pablo Aguirre, Bernd Krauskopf & Hinke M. Osinga
   to appear in Journal of Computational Dynamics
   
   
2. Continuation-based numerical detection of after-depolarization and spike-adding thresholds (abstract, preprint)
   Jakub Nowacki, Hinke M. Osinga & Krasimira T. Tsaneva-Atanasova
   Neural Computation 25(4): 877–900, 2013.
   
   
3. Dynamical systems analysis of spike-adding mechanisms in transient bursts (abstract, preprint)
   Jakub Nowacki, Hinke M. Osinga & Krasimira T. Tsaneva-Atanasova
   The Journal of Mathematical Neuroscience 2: 7, 2012.
   
   

4. Mixed-mode oscillations with multiple time scales (abstract, preprint) Mathieu Desroches, John Guckenheimer, Bernd Krauskopf, Christian Kuehn, Hinke M. Osinga & Martin Wechselberger SIAM Review 54(2): 211–288, 2012.

   
   
   
5. The singular limit of a Hopf bifurcation (abstract, preprint)
   John Guckenheimer & Hinke M. Osinga
   Discrete and Continuous Dynamical Systems – Series A 32(8): 2805–2823, 2012.
   
   
6. Cross-currents between biology and mathematics: The codimension of pseudo-plateau bursting (abstract, preprint)
   Hinke M. Osinga, Arthur Sherman & Krasimira T. Tsaneva-Atanasova
   Discrete and Continuous Dynamical Systems – Series A 32(8): 2853–2877, 2012.
   
   
7. Global invariant manifolds in the transition to preturbulence in the Lorenz system (abstract, preprint)
   Eusebius J. Doedel, Bernd Krauskopf & Hinke M. Osinga
   Indagationes Mathematicae 22(3–4): 222–240, 2011.
   
   
8. Exploring the dynamics of a class of post-tensioned, moment resisting frames (abstract, preprint)
   Nick A. Alexander, Olafur Oddbjornsson, Colin A. Taylor, Hinke M. Osinga & David E. Kelly
   Journal of Sound and Vibration 330(15): 3710–3728, 2011.
   
   
9. A unified model of CA1/3 pyramidal cells: An investigation into excitability (abstract, preprint)
   Jakub Nowacki, Hinke M. Osinga John T. Brown Andrew D. Randall & Krasimira T. Tsaneva-Atanasova
   Progress in Biophysics and Molecular Biology 105(1-2): 34–48, 2011.
   
   
10. Investigating the consequences of global bifurcations for two-dimensional invariant manifolds of vector fields (abstract, preprint)
    Pablo Aguirre, Eusebius J. Doedel, Bernd Krauskopf & Hinke M. Osinga
    Discrete and Continuous Dynamical Systems – Series A 29(4): 1309–1344, 2011.
    
    
11. Understanding anomalous delays in a model of intracellular calcium dynamics (abstract, preprint)
    Emily Harvey, Vivien Kirk, Hinke M. Osinga, James Sneyd & Martin Wechselberger
    Chaos 20(4): 045104, 2010.
    
    
12. Dynamics of plateau bursting in dependence on the location of its equilibrium (abstract, preprint)
    Hinke M. Osinga & Krasimira T. Tsaneva-Atanasova
    Journal of Neuroendocrinology 22(12): 1301–1314, 2010.
    
    
13. Modeling mechanisms of cell secretion (abstract, preprint)
    Krasimira T. Tsaneva-Atanasova, Hinke M. Osinga, Joel Tabak & Morten Gram Pedersen
    Acta Biotheoretica 58(4): 315–327, 2010.
    
    
14. A continuation method for computing global isochrons (abstract, preprint)
    Hinke M. Osinga & Jeff Moehlis
    SIAM Journal on Applied Dynamical Systems 9(4): 1201–1228, 2010.
    
    
15. Full system bifurcation analysis of endocrine bursting models (abstract, preprint)
    Krasimira T. Tsaneva-Atanasova, Hinke M. Osinga, Thorsten Rieß & Arthur Sherman
    Journal of Theoretical Biology 264(4): 1133–1146, 2010.
    
    
16. The role of large-conductance Calcium-activated K⁺ (BK) channels in shaping bursting oscillations of a somatotroph cell model (abstract, preprint)
    Jakub Nowacki, Siti H. Mazlan, Hinke M. Osinga & Krasimira T. Tsaneva-Atanasova
    Physica D 239(9): 485–493 2010.
    
    
17. Numerical continuation of canard orbits in slow-fast dynamical systems (abstract, preprint)
    Mathieu Desroches, Bernd Krauskopf & Hinke M. Osinga
    Nonlinearity 23(3): 739–765, 2010; with multimedia supplement.
    
    
18. Arnol'd tongues arising from a grazing-sliding bifurcation (abstract, preprint)
    Róbert Szalai & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 8(4): 1434–1461, 2009.
    
    
19. The geometry of mixed-mode oscillations in the Olsen model for peroxidase-oxidase reaction (abstract, preprint)
    Mathieu Desroches, Bernd Krauskopf & Hinke M. Osinga
    Discrete and Continuous Dynamical Systems — Series S 2(4): 807–827, 2009.
    
    
20. Codimension-one tangency bifurcations of global Poincaré maps of four-dimensional vector fields (abstract, preprint)
    Bernd Krauskopf, Clare M. Lee & Hinke M. Osinga
    Nonlinearity 22(5): 1091–1121, 2009.
    
    
21. The geometry of slow manifolds near a folded node (abstract, preprint)
    Mathieu Desroches, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 7(4): 1131–1162, 2008.
    
    
22. Bifurcations of the global stable set of a planar endomorphism near a cusp singularity (abstract, preprint)
    Catherine A. Hobbs & Hinke M. Osinga
    Int. J. Bifurcation & Chaos 18(8): 2207–2222, 2008.
    
    
23. Tangency bifurcations of global Poincaré maps (abstract, preprint)
    Clare M. Lee, Pieter J. Collins, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 7(3): 712–754, 2008.
    
    
24. Invariant polygons in systems with grazing-sliding (abstract, preprint)
    Róbert Szalai & Hinke M. Osinga
    Chaos 18(2): 023121, 2008.
    
    
25. 
    

    Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh Nagumo system (abstract, preprint) Mathieu Desroches, Bernd Krauskopf & Hinke M. Osinga Chaos 18(1): 015107, 2008.

    
    
26. Unstable manifolds of a limit cycle near grazing (abstract, preprint)
    Róbert Szalai & Hinke M. Osinga
    Nonlinearity 21(2): 273–284, 2008.
    
    
27. Resetting behavior in a model of bursting in secretory pituitary cells: Distinguishing plateaus from pseudo-plateaus (abstract, preprint)
    Julie V. Stern, Hinke M. Osinga, Andrew LeBeau & Arthur Sherman
    Bulletin of Mathematical Biology 70(1): 68–88, 2008.
    
    
28. Efficient computation of quasiperiodic oscillations in nonlinear systems with fast rotating parts (abstract, preprint)
    Frank Schilder, Jan Rübel, Jens Starke, Hinke M. Osinga, Bernd Krauskopf & Mizuho Inagaki
    Nonlinear Dynamics 51(4): 529–539, 2008.
    
    
29. Visualizing curvature on the Lorenz manifold (abstract, preprint)
    Hinke M. Osinga & Bernd Krauskopf
    Journal of Mathematics and the Arts 1(2): 113–123, 2007.
    
    
30. Unfolding the cusp-cusp bifurcation of planar endomorphisms (abstract, preprint)
    Bernd Krauskopf, Hinke M. Osinga & Bruce B. Peckham
    SIAM Journal on Applied Dynamical Systems 6(2): 403–440, 2007.
    
    
31. Computing two-dimensional global invariant manifolds in slow-fast systems (abstract, preprint)
    James P. England, Bernd Krauskopf & Hinke M. Osinga
    Int. J. Bifurcation & Chaos 17(3): 805–822, 2007.
    
    
32. Global bifurcations of the Lorenz manifold (abstract, preprint)
    Eusebius J. Doedel, Bernd Krauskopf & Hinke M. Osinga
    Nonlinearity 19(12): 2947–2972, 2006; with multimedia supplement.
    
    
33. Boundary crisis bifurcation in two parameters (abstract, preprint)
    Hinke M. Osinga
    Journal of Difference Equations and Applications 12(10): 997–1008, 2006.
    
    
34. The geometry of the solution set of nonlinear optimal control problems (abstract, preprint)
    Hinke M. Osinga & John Hauser
    Journal of Dynamics and Differential Equations 18(4): 881–900, 2006.
    
    
35. Locus of boundary crisis: Expect infinitely many gaps (abstract, preprint)
    Hinke M. Osinga
    Phys. Rev. E 74(3): 035201(R), 2006.
    
    
36. Fourier methods for quasi-periodic oscillations (abstract, preprint)
    Frank Schilder, Werner Vogt, Stephan Schreiber & Hinke M. Osinga
    International Journal for Numerical Methods in Engineering 67(5): 629–671, 2006.
    
    
37. Computing one-dimensional global manifolds of Poincaré maps by continuation (abstract, preprint)
    James P. England, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 4(4): 1008–1041, 2005.
    
    
38. Continuation of quasi-periodic invariant tori (abstract, preprint)
    Frank Schilder, Hinke M. Osinga & Werner Vogt
    SIAM Journal on Applied Dynamical Systems 4(3): 459–488, 2005.
    
    
39. Bifurcations and limit dynamics in adaptive control systems (abstract, preprint)
    G. Reza Rokni Lamooki, Stuart Townley & Hinke M. Osinga
    Int. J. Bifurcation & Chaos 15(5): 1641–1664, 2005.
    
    
40. Bifurcations of stable sets in noninvertible planar maps (abstract, preprint)
    James P. England, Bernd Krauskopf & Hinke M. Osinga
    Int. J. Bifurcation & Chaos 15(3): 891–904, 2005.
    [Reprinted in E.J. Doedel, G. Domokos and I.G. Kevrekidis (Eds.), Modeling and Computations in Dynamical Systems, World Scientific (2006), pp. 195–208]
    
    
41. 
    

    A survey of methods for computing (un)stable manifolds of vector fields (abstract, preprint) Bernd Krauskopf, Hinke M. Osinga, Eusebius J. Doedel, Michael E. Henderson, John M. Guckenheimer, Alexander Vladimirsky, Michael Dellnitz & Oliver Junge Int. J. Bifurcation & Chaos 15(3): 763–791, 2005. [Reprinted in E.J. Doedel, G. Domokos and I.G. Kevrekidis (Eds.), Modeling and Computations in Dynamical Systems, World Scientific (2006), pp. 67–95]

    
    
42. Two-dimensional invariant manifolds in four-dimensional dynamical systems (abstract, preprint)
    Hinke M. Osinga
    Computers & Graphics 29(2): 289–297, 2005.
    
    
43. 
    

    Crocheting the Lorenz manifold (preprint) Hinke M. Osinga & Bernd Krauskopf The Mathematical Intelligencer 26(4): 25–37, 2004 (Crochet instructions).

    
    
44. Numerical approximations of strong (un)stable manifolds (abstract, preprint)
    Hinke M. Osinga, G. Reza Rokni Lamooki & Stuart Townley
    Dynamical Systems 19(3): 195–215, 2004.
    
    
45. Computing one-dimensional stable manifolds of planar maps without the inverse (abstract, preprint)
    James P. England, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 3(2): 161–190, 2004.
    
    
46. A set oriented approach to global optimal control (abstract, preprint)
    Oliver Junge & Hinke M. Osinga
    ESAIM: Control, Optimisation and Calculus of Variations 10(2): 259–270, 2004.
    
    
47. 
    

    The Lorenz manifold as a collection of geodesic level sets (abstract) Bernd Krauskopf & Hinke M. Osinga Nonlinearity 17(1): C1–C6, 20046; with multimedia supplement.

    
    
48. Computing geodesic level sets on global (un)stable manifolds of vector fields (abstract, preprint)
    Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 2(4): 546–569, 2003.
    
    
49. 
    

    Nonorientable manifolds of three-dimensional vector fields (abstract, preprint) Hinke M. Osinga Int. J. Bifurcation & Chaos 13(3): 553–570, 2003.

    
    
50. Visualizing the structure of chaos in the Lorenz system (abstract, preprint)
    Hinke M. Osinga & Bernd Krauskopf
    Computers & Graphics 26(5): 815–823, 2002.
    
    
51. Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map (abstract, preprint)
    Hinke M. Osinga, Jan Wiersig, Paul Glendinning & Ulrike Feudel
    Int. J. Bifurcation & Chaos 11(12): 3085–3105, 2001.
    
    
52. Boundary crisis in quasiperiodically forced systems (abstract, preprint)
    Hinke M. Osinga & Ulrike Feudel
    Physica D 141(1-2): 54–64, 2000.
    
    
53. Two-dimensional global manifolds of vector fields (abstract, preprint)
    Bernd Krauskopf & Hinke M. Osinga
    Chaos 9(3): 768–774, 1999; with multimedia supplement.
    
    
54. Growing 1D and quasi 2D unstable manifolds of maps (abstract, preprint)
    Bernd Krauskopf & Hinke M. Osinga
    J. Comput. Phys. 146(1): 404–419, 1998; see also the multimedia supplement in VUTH eprint 98-21.
    
    
55. 
    

    Globalizing two-dimensional unstable manifolds of maps (abstract, multimedia preprint) Bernd Krauskopf & Hinke M. Osinga Int. J. Bifurcation & Chaos 8(3): 483–503, 1998.

    
    
56. Algorithms for computing normally hyperbolic invariant manifolds (abstract)
    Henk W. Broer, Hinke M. Osinga & Gert Vegter
    Z. angew. Math. Phys. 48(3): 480–524, 1997.
    
    
57. On the computation of invariant manifolds of fixed points (abstract)
    Ale Jan Homburg, Hinke M. Osinga & Gert Vegter
    Z. angew. Math. Phys. 46(2): 171–187, 1995.
    
    

Book Chapters

1. Interview with Herbert Bishop Keller
   Hinke M. Osinga
   in A. Bultheel and R. Cools (Eds.), The birth of numerical analysis, World Scientific (2010), pp. 45–52.
   
   
2. Computing invariant manifolds via the continuation of orbit segments
   Bernd Krauskopf & Hinke M. Osinga
   in B. Krauskopf, H.M. Osinga and J. Galán-Vioque (Eds.), Numerical Continuation Methods for Dynamical Systems: Path following and boundary value problems, Springer-Verlag (2007), pp. 117–154.
   
   
3. Bifurcations of stable sets in noninvertible planar maps
   James P. England, Bernd Krauskopf & Hinke M. Osinga
   in E.J. Doedel, G. Domokos and I.G. Kevrekidis (Eds.), Modeling and Computations in Dynamical Systems, World Scientific Series on Nonlinear Science B 13, World Scientific (2006), pp. 195–208. [Reprinting of Int. J. Bifurcation & Chaos 15(3): 891–904, 2005]
   
   
4. 
   

   A survey of methods for computing (un)stable manifolds of vector fields Bernd Krauskopf, Hinke M. Osinga, Eusebius J. Doedel, Michael E. Henderson, John M. Guckenheimer, Alexander Vladimirsky, Michael Dellnitz & Oliver Junge in E.J. Doedel, G. Domokos and I.G. Kevrekidis (Eds.), Modeling and Computations in Dynamical Systems, World Scientific Series on Nonlinear Science B 13, World Scientific (2006), pp. 67–95. [Reprinting of Int. J. Bifurcation & Chaos 15(3): 763–791, 2005]

   
   
   

Publications in Refereed Proceedings

1. Two-Parameter locus of boundary crisis: mind the gaps! (preprint)
   Hinke M. Osinga & James Rankin
   in Wei Feng, Zhaosheng Feng, Maurizio Grasselli, Akif Ibragimov, Xin Lu, Stefan Siegmund and Jürgen Voigt (Eds.), Proceedings of The 8th AIMS international conference, American Institue of Mathematical Sciences, pp. 1148–1157, 2011.
   
   
2. Visualizing global manifolds during the transition to chaos in the Lorenz system (Combined preprints BCANM.879 BCANM.878.)
   Bernd Krauskopf, Hinke M. Osinga & Eusebius J. Doedel
   in H.-C. Hege, K. Polthier and G. Scheuermann (Eds.), Topology-Based Methods in Visualization II, Springer-Verlag, pp. 115–126, 2009.
   
   
3. The sculpture Manifold: a band from a surface, a surface from a band (preprint)
   Bernd Krauskopf, Hinke M. Osinga & Benjamin Storch
   in Reza Sarhangi and Carlo Séquin (Eds.) Proceedings of Bridges Leeuwarden: Mathematical Connections in Art, Music, and Science, Leeuwarden, pp. 9–14, 2008.
   
   
4. The Lorenz manifold: crochet and curvature (preprint)
   Hinke M. Osinga & Bernd Krauskopf
   in Reza Sarhangi and John Sharp (Eds.) Proceedings of Bridges London: Mathematical Connections in Art, Music, and Science, London, pp. 255–260, 2006.
   
   
5. Separating manifolds in slow-fast systems (preprint)
   Hinke M. Osinga & James P. England
   in D.H. van Campen, M.D. Lazurko, and W.P.J.M. van den Oever (Eds.) Proceedings of the Fifth EUROMECH Nonlinear Dynamics Conference, ENOC 2005, Eindhoven, ID 15-454, pp. 1699–1705, 2005.
   
   
6. 
   

   Geodesic parametrization of global invariant manifolds, or what does the Equadiff 2003 poster show? (preprint) Bernd Krauskopf & Hinke M. Osinga in F. Dumortier, H.W. Broer, J. Mawhin, A. Vanderbauwhede and S. Verduyn Lunel (Eds.) Proceedings of the International Conference on Differential Equations, Equadiff 2003, Hasselt, pp. 429–433, World Scientific, Singapore, 2005.

   
   
7. 
   

   Numerical study of manifold computations(preprint) Hinke M. Osinga & G. Reza Rokni Lamooki in F. Dumortier, H.W. Broer, J. Mawhin, A. Vanderbauwhede and S. Verduyn Lunel (Eds.) Proceedings of the International Conference on Differential Equations, Equadiff 2003, Hasselt, pp. 190–195, World Scientific, Singapore, 2005.

   
   
8. On the geometry of optimal control: the inverted pendulum example (Multimedia site)
   John Hauser & Hinke M. Osinga
   in Proceedings of the American Control Conference, Arlington VA, USA, Volume 2, pp. 1721–1726, 2001.
   
   
9. Non-orientable manifolds of periodic orbits (abstract)
   Hinke M. Osinga
   in B. Fiedler, K. Gröger and J. Sprekels (Eds.) Proceedings of the International Conference on Differential Equations Volume 2, Equadiff 99, Berlin, pp. 922–924, World Scientific, Singapore, 2000.
   
   
10. Investigating torus bifurcations in the forced Van der Pol oscillator (abstract)
    Bernd Krauskopf & Hinke M. Osinga
    in E.J. Doedel and L.S. Tuckerman (Eds.) Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, IMA Volumes in Mathematics and its Applications 119, pp. 199–208, Springer-Verlag, 2000.
    
    
11. Computing a normally attracting invariant manifold of a Poincaré map
    Henk W. Broer, Hinke M. Osinga & Gert Vegter
    in P.L. Butzer, H.Th. Jongen and W. Oberschelp (Eds.), Charlemagne and His Heritage, 1200 Years of Civilization and Science in Europe, Volume 2: Mathematical Arts, pp. 541–549, Brepols Publishers, 1998.
    
    
12. On the computation of normally hyperbolic invariant manifolds
    Henk W. Broer, Hinke M. Osinga & Gert Vegter
    in H.W. Broer, S.A. van Gils, I. Hoveijn and F. Takens (Eds.), Nonlinear Dynamical Systems and Chaos, Progress in Nonlinear Differential Equations and Their Applications 19, pp. 423–447, Birkhäuser Verlag, Basel / Switzerland, 1996.
    
    
13. Computing a normally hyperbolic invariant manifold of saddle type
    Henk W. Broer, Hinke M. Osinga & Gert Vegter
    in G.S. Ladde and M. Sambandham (Eds.), Proceedings of Dynamic Systems & Applications 2, pp. 83–90, Dynamic Publishers, 1996.
    
    
14. Comparison of robustly stabilizing controllers for a flexible beam model with additive, multiplicative and stable factor perturbations
    J. Bontsema, R.F. Curtain, C.R. Kuiper & Hinke M. Osinga
    in R. Curtain, A. Bensoussan and J.L. Lions (Eds.), Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite Dimensional Systems, Proc. of the 10th International Conference on Analysis and Optimization, June 1992, Sophia-Antipolis, France, Lecture Notes in Control and Information Sciences 185, pp. 388–400, Springer-Verlag, 1993.
    
    
    

Other Publications

1. 
   

   Chaos and Crochet Hinke M. Osinga, DVD in the series of LMS Popular Lectures, produced by mathMedia for The London Mathematical Society, 2007; available from the LMS.

   
   
2. Engineering neurons
   Hinke M. Osinga, in C. Lewis (Ed.) re: search, University of Bristol Research Review, issue 13 (PDF), 2006.
   
   
3. 
   

   Maths looks good Hinke M. Osinga, in S. Franklin, S. Williams and Z. Longridge-Berry (Eds.) Extra, the University of Exeter quarterly newsletter, Spring issue, 2000.

   
   
4. 
   

   March poster as part of the series Posters in the London Underground celebrating the World Mathematics Year, design by Andrew Burbanks, Bernd Krauskopf & Hinke M. Osinga, organised by the Isaac Newton Institute for Mathematical Sciences with support from EPSRC, 2000.

   
   
5. One-dimensional strong stable and unstable manifolds code
   Hinke M. Osinga & G. Reza Rokni Lamooki, software for use inside the Tcl/Tk version of DsTool, available via http://www.dynamicalsystems.org/sw/sw/detail?item=26.
   
   
6. Global Manifold 1D code, version 2
   Hinke M. Osinga & James P. England, software for use inside the Tcl/Tk version of DsTool, available via http://www.dynamicalsystems.org/sw/sw/detail?item=27.
   
   
   

Preprints

1. Strategy and sub-strategy dynamics in an evolutionary game (preprint)
   Hinke M. Osinga & James A.R. Marshall
   Preprint, The University of Auckland, 2013.
   
   
2. Geometric analysis of transient bursts (preprint)
   Hinke M. Osinga & Krasimira T. Tsaneva-Atanasova
   Preprint, The University of Auckland, 2013.
   
   
3. Interacting global invariant sets in a planar map model of wild chaos (preprint)
   Stefanie Hittmeyer, Bernd Krauskopf & Hinke M. Osinga
   Preprint, The University of Auckland, 2013.
   
   
4. Global invariant manifolds near homoclinic orbits to a real saddle: (non)orientability and flip bifurcation (preprint)
   Pablo Aguirre, Bernd Krauskopf & Hinke M. Osinga
   Preprint, The University of Auckland, 2013.
   
   
5. Growing unstable manifolds of planar maps
   Bernd Krauskopf & Hinke M. Osinga
   IMA preprint 1517, 1997.