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. Slow negative feedback enhances robustness of square-wave bursting (abstract, preprint)
    Sushmita Rose John, Bernd Krauskopf, Hinke M. Osinga, & Jonathan E. Rubin
    Journal of Computational Neuroscience 51(2): 239–261, 2023.

  2. Boxing-in of a blender in a Hénon-like family (abstract, preprint)
    Stefanie Hittmeyer, Bernd Krauskopf, Hinke M. Osinga & Katsutoshi Shinohara,
    Frontiers in Applied Mathematics and Statistics – Section Dynamical Systems 9: 1086240, 2023

  3. Isochron foliations and global bifurcations: A case study (abstract, preprint)
    James Hannam, Bernd Krauskopf & Hinke M. Osinga
    Transactions of Mathematics and Its Applications 6(2): 1–43, 2022; with Coco code and implementation manual.

  4. Determining the global manifold structure of a continuous-time heterodimensional cycle (abstract, preprint)
    Andy Hammerlindl, Bernd Krauskopf, Gemma Mason & Hinke M. Osinga
    Journal of Computational Dynamics 9(3):393–419, 2022.

  5. Matching geometric and expansion characteristics of wild chaotic attractors (abstract, preprint)
    Hamish Jelleyman & Hinke M. Osinga
    The European Physical Journal—Special Topics 231(3):403–412, 2022.

  6. Numerical continuation of spiral waves in heteroclinic networks of cyclic dominance (abstract, preprint)
    Cris R. Hasan, Hinke M. Osinga, Claire M. Postlethwaite, & Alastair M. Rucklidge
    IMA Journal of Applied Mathematics 86(5):1141–1163, 2021.

  7. Stability of periodic travelling waves in a Rock-Paper-Scissors model (abstract, preprint)
    Cris R. Hasan, Hinke M. Osinga, Claire M. Postlethwaite, & Alastair M. Rucklidge
    Nonlinearity 34(8):5576–5598, 2021.

  8. How to identify a hyperbolic set as a blender (abstract, preprint)
    Stefanie Hittmeyer, Bernd Krauskopf, Hinke M. Osinga & Katsutoshi Shinohara
    Discrete and Continuous Dynamical Systems—Series A 40(12): 6815–6836, 2020.

  9. A surface of heteroclinic connections between two saddle slow manifolds in the Olsen model (abstract, preprint)
    Elle Musoke, Bernd Krauskopf, and Hinke M. Osinga
    Int. J. Bifurcation & Chaos 30(16): 2030048, 2020.

  10. Computing connecting orbits to infinity associated with a homoclinic flip bifurcation (abstract, preprint)
    Andrus Giraldo, Bernd Krauskopf & Hinke M. Osinga
    Journal on Computational Dynamics 7(2): 489–510, 2020.

  11. Cascades of global bifurcations and chaos near a homoclinic flip bifurcation: a case study (abstract, preprint)
    Andrus Giraldo, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 17(4) : 2784–2829, 2018.

  12. Interactions between a locally separating stable manifold and a bursting periodic orbit (abstract, preprint)
    Saeed Farjami, Vivien Kirk & Hinke M. Osinga
    The European Physical Journal Special Topics 227(5–6): 603–614, 2018.

  13. Existence of blenders in a Hénon-like family: geometric insights from invariant manifold computations (abstract, preprint)
    Stefanie Hittmeyer, Bernd Krauskopf, Hinke M. Osinga & Katsutoshi Shinohara,
    Nonlinearity 31(10): R239–R267, 2018.

  14. Tangencies between global invariant manifolds and slow manifolds near a singular Hopf bifurcation (abstract, preprint)
    José Mujica, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 17(2) : 1395–1431, 2018.

  15. Saddle slow manifolds and canard orbits in R4 and application to the full Hodgkin–Huxley model (abstract, preprint)
    Cris R. Hasan, Bernd Krauskopf & Hinke M. Osinga
    The Journal of Mathematical Neuroscience 8: 5, 2018.

  16. Understanding the geometry of dynamics: The stable manifold of the Lorenz system (abstract, preprint)
    Hinke M. Osinga
    Journal of the Royal Society of New Zealand, 48(2–3): 203–214, 2018.

  17. Computing the stable manifold of a saddle slow manifold (abstract, preprint)
    Saeed Farjami, Vivien Kirk, & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 17(1): 350–379, 2018.

  18. Natural extension of fast-slow decomposition for dynamical systems (abstract, preprint)
    Jonathan E. Rubin, Bernd Krauskopf & Hinke M. Osinga
    Physical Review E 97(1): 012215, 2018.

  19. A Lin's method approach for detecting canard orbits near a folded node (abstract, preprint)
    José Mujica, Bernd Krauskopf & Hinke M. Osinga
    Journal of Computational Dynamics 4(1&2): 143–165, 2017.

  20. Mixed-mode oscillations and twin canard orbits in an autocatalytic chemical reaction (abstract, preprint)
    Cris R. Hasan, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 16(4): 2165–2195, 2017.

  21. Finding first foliation tangencies in the Lorenz system (abstract, preprint)
    Jennifer L. Creaser, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 16(4): 2127–2164, 2017.

  22. Parameter-dependent behaviour of periodic channels in a locus of boundary crisis (abstract, preprint)
    James Rankin & Hinke M. Osinga
    The European Physical Journal Special Topics 226(9): 1739–1750, 2017.

  23. Saddle invariant objects and their global manifolds in a neighborhood of a homoclinic flip bifurcation of case B (abstract, preprint)
    Andrus Giraldo, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 16(1): 640–686, 2017.

  24. Global isochrons of a planar system near a phaseless set with saddle equilibria (abstract, preprint)
    James Hannam, Bernd Krauskopf & Hinke M. Osinga
    The European Physical Journal Special Topics 225(13): 2645–2654, 2016.

  25. Transient spike adding in the presence of equilibria (abstract, preprint)
    Saeed Farjami, Vivien Kirk & Hinke M. Osinga
    The European Physical Journal Special Topics 225(13): 2601–2612, 2016.

  26. From wild Lorenz-like to wild Rovella-like dynamics (abstract, preprint)
    Stefanie Hittmeyer, Bernd Krauskopf & Hinke M. Osinga
    Dynamical Systems 30(4): 525–542, 2015.

  27. Global organization of phase space in the transition to chaos in the Lorenz system (abstract, preprint)
    Eusebius J. Doedel, Bernd Krauskopf & Hinke M. Osinga
    Nonlinearity 28(11): R113–R139, 2015; with multimedia supplement.

  28. Forward-time and backward-time isochrons, and their interactions (abstract, preprint)
    Peter Langfield, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 14(3): 1418–1453, 2015.

  29. Interactions of the Julia set with critical and (un)stable sets in an angle-doubling map on \({\mathbb C}\setminus\{0\}\) (abstract, preprint)
    Stefanie Hittmeyer, Bernd Krauskopf & Hinke M. Osinga
    Int. J. Bifurcation & Chaos 25(4): 1530013, 2015.

  30. Invariant manifolds and global bifurcations (abstract, preprint)
    John Guckenheimer, Bernd Krauskopf, Hinke M. Osinga & Björn Sandstede
    Chaos 25(9): 097604, 2015.

  31. Adaptive topographies and equilibrium selection in an evolutionary game (abstract, preprint)
    Hinke M. Osinga & James A.R. Marshall
    PLoS One 10(2): e0116307, 2015.

  32. α-flips and T-points in the Lorenz system (abstract, preprint)
    Jennifer L. Creaser, Bernd Krauskopf & Hinke M. Osinga
    Nonlinearity 28(3): R39–R65, 2015; with multimedia supplement.

  33. Bifurcation analysis of a smoothed model of a forced impacting beam and comparison with an experiment (abstract, preprint)
    Michael Elmegård, Bernd Krauskopf, Hinke M. Osinga, Jens Starke & Jon J. Thomsen
    Nonlinear Dynamics 77(3): 951–966, 2014.

  34. Global invariant manifolds near a Shilnikov homoclinic bifurcation (abstract, preprint)
    Pablo Aguirre, Bernd Krauskopf & Hinke M. Osinga
    Journal of Computational Dynamics 1(1): 1–38, 2014.

  35. Solving Winfree's puzzle: the isochrons in the FitzHugh-Nagumo model (abstract, preprint)
    Peter Langfield, Bernd Krauskopf & Hinke M. Osinga
    Chaos 24(1): 013131, 2014.

  36. Geometric analysis of transient bursts (abstract, preprint)
    Hinke M. Osinga & Krasimira T. Tsaneva-Atanasova
    Chaos 23(4): 046107, 2013.

  37. Global invariant manifolds near homoclinic orbits to a real saddle: (non)orientability and flip bifurcation (abstract, preprint)
    Pablo Aguirre, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 12(4): 1803–1846, 2013.

  38. Interacting global invariant sets in a planar map model of wild chaos (abstract, preprint)
    Stefanie Hittmeyer, Bernd Krauskopf & Hinke M. Osinga
    SIAM Journal on Applied Dynamical Systems 12(3): 1280–1329, 2013.

  39. 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.

  40. 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.

  41.   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.


  42. 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.

  43. 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.

  44. 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.

  45. Exploring the dynamics of a class of post-tensioned, moment resisting frames (abstract)
    Nick A. Alexander, Olafur Oddbjornsson, Colin A. Taylor, Hinke M. Osinga & David E. Kelly
    Journal of Sound and Vibration 330(15): 3710–3728, 2011.

  46. A unified model of CA1/3 pyramidal cells: An investigation into excitability (abstract, preprint)
    Jakub Nowacki, Hinke M. Osinga Johnathan T. Brown Andrew D. Randall & Krasimira T. Tsaneva-Atanasova
    Progress in Biophysics and Molecular Biology 105(1-2): 34–48, 2011.

  47. 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.

  48. 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.

  49. 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.

  50. 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.

  51. 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; multimedia material also available via University of Bristol preprint site.

  52. 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.

  53. 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.

  54. 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.

  55. 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; multimedia material also available via University of Bristol preprint site.

  56. 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.

  57. 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.

  58. 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; multimedia material also available via University of Bristol preprint site.

  59. 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.

  60. 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; multimedia material also available via University of Bristol preprint site.

  61. Invariant polygons in systems with grazing-sliding (abstract, preprint)
    Róbert Szalai & Hinke M. Osinga
    Chaos 18(2): 023121, 2008.


  62.   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.

  63. Unstable manifolds of a limit cycle near grazing (abstract, preprint)
    Róbert Szalai & Hinke M. Osinga
    Nonlinearity 21(2): 273–284, 2008.

  64. 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.

  65. 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.

  66. Visualizing curvature on the Lorenz manifold (abstract, preprint)
    Hinke M. Osinga & Bernd Krauskopf
    Journal of Mathematics and the Arts 1(2): 113–123, 2007.

  67. 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.

  68. 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.

  69. 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.

  70. Boundary crisis bifurcation in two parameters (abstract, preprint)
    Hinke M. Osinga
    Journal of Difference Equations and Applications 12(10): 997–1008, 2006.

  71. 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; see also multimedia material from the University of Bristol preprint site.

  72. Locus of boundary crisis: Expect infinitely many gaps (abstract, preprint)
    Hinke M. Osinga
    Physical Review E 74(3): 035201(R), 2006.

  73. 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.

  74. 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.

  75. 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.

  76. 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.

  77. 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]


  78.   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]

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


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

  81. Numerical approximations of strong (un)stable manifolds (abstract)
    Hinke M. Osinga, G. Reza Rokni Lamooki & Stuart Townley
    Dynamical Systems 19(3): 195–215, 2004.

  82. 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.

  83. 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.


  84.   The Lorenz manifold as a collection of geodesic level sets (abstract)
    Bernd Krauskopf & Hinke M. Osinga
    Nonlinearity 17(1): C1–C6, 2004; with multimedia supplement.

  85. 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; see also a copy of the multimedia material. (Note: preprint BCANM_99r2r is an older version.)


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

  87. Visualizing the structure of chaos in the Lorenz system (abstract, preprint)
    Hinke M. Osinga & Bernd Krauskopf
    Computers & Graphics 26(5): 815–823, 2002.

  88. 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.

  89. Boundary crisis in quasiperiodically forced systems (abstract, preprint)
    Hinke M. Osinga & Ulrike Feudel
    Physica D 141(1-2): 54–64, 2000.

  90. Two-dimensional global manifolds of vector fields (abstract, preprint)
    Bernd Krauskopf & Hinke M. Osinga
    Chaos 9(3): 768–774, 1999; with multimedia supplement.

  91. Growing 1D and quasi 2D unstable manifolds of maps (abstract, preprint)
    Bernd Krauskopf & Hinke M. Osinga
    Journal of Computational Physics 146(1): 404–419, 1998; see also the multimedia supplement in VUTH eprint 98-21.


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

  93. 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.

  94. 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. A heteroclinc surface between two saddle slow manifolds organizing sectors of rotation of mixed-mode oscillations (preprint)
    Elle Musoke, Bernd Krauskopf & Hinke M. Osinga
    to appear in H. Jardón-Kojakhmetov, M. Engel, B. Sandstede and C. Soresina (Eds.), Topics in Multiple Time Scale Dynamics, Contemporary Mathematics, American Mathematical Society.

  2. Global manifolds of saddle periodic orbits parametrised by isochrons (preprint)
    James Hannam, Bernd Krauskopf & Hinke M. Osinga
    to appear in S. Olaru, S. Elaydi, J. Cushing and R. Lozi (Eds.) Advances in Discrete Dynamical Systems, Difference Equations, and Applications, ICDEA 2022, Springer Proceedings in Mathematics and Statistics, Springer Nature.

  3. A continuation approach to computing phase resetting curves (preprint)
    Peter Langfield, Bernd Krauskopf & Hinke M. Osinga
    in O. Junge, O. Schütze, G. Froyland S. Ober-Blobaum and K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer-Verlag (2020), pp. 3–30.

  4. Generalized Mandelbrot and Julia sets in a family of planar angle-doubling maps (preprint, Contents online)
    Stefanie Hittmeyer, Bernd Krauskopf & Hinke M. Osinga
    in M. Bohner, S. Siegmund, R.Š. Hilscher and P. Stehlík (Eds.) Difference Equations and Discrete Dynamical Systems with Applications, ICDEA 2018, Springer Proceedings in Mathematics and Statistics, Springer Nature (2020), pp. 21–54.

  5. A mathematical approach to computing structural-failure boundaries (preprint, CRC Press)
    Hinke M. Osinga
    in N. Chouw, R.P. Orense and T. Larkin (Eds.), International Workshop on Seismic Performance of Soil-Foundation-Structure Systems, CRC Press (2017), pp. 89–97.

  6. A codimension-four singularity with potential for action (preprint, Springer online)
    Bernd Krauskopf & Hinke M. Osinga
    in B. Toni (Ed.), Interdisciplinary Mathematical Research and Applications, In Honor of Professor Christiane Rousseau. And In Recognition of the Mathematics for Planet Earth Initiative, Springer Proceedings in Mathematics and Statistics 157, Springer-Verlag (2016), pp. 253–268.

  7. Chaos and wild chaos in Lorenz-type systems (preprint, Contents online)
    Hinke M. Osinga, Bernd Krauskopf & Stefanie Hittmeyer
    in Z. Al-Sharawi, J.M. Cushing and S. Elaydi (Eds.) Theory and Applications of Difference Equations and Discrete Dynamical Systems, ICDEA 2013, Springer Proceedings in Mathematics and Statistics 102, Springer-Verlag (2014), pp. 75–98.

  8. Computing global invariant manifolds: Techniques and applications (preprint, official ICM online version)
    Hinke M. Osinga
    in S.Y. Jang, Y.R. Kim, D.-W. Lee and I. Yie (Eds.), Proceedings of the International Congress of Mathematicians Seoul 2014, Kyung Moon SA publishers (2014), Volume IV, pp. 1101–1123.

  9. 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; this interview first appeared in DSWeb Magazine, April 2005.

  10. 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.

  11. 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.

  12. 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]


  13.   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. Generalized Julia sets: from Cantor bouquet to Cantor cheese (preprint)
    Stefanie Hittmeyer, Bernd Krauskopf & Hinke M. Osinga
    in Proceedings Bridges Conference on Mathematics and the Arts, Linz, Austria, 2019; paper #2019-371.

  2. A new approach to modelling structural responses to earthquakes (paper)
    Hanlu (Annabelle) Xu, Xiaoyang (Gary) Qin, N. Chouw, T. Larkin and H.M. Osinga
    in Proceedings of the 2018 New Zealand Society for Earthquake Engineering, Auckland, 2018, #P1.07 (7 pages)

  3. Shake table simulation of dynamic forces of a structure (paper)
    Xiaoyang (Gary) Qin, Hanlu (Annabelle) Xu, N. Chouw, T. Larkin and H.M. Osinga
    in Proceedings of the 2018 New Zealand Society for Earthquake Engineering, Auckland, 2018, #O3C.2 (8 pages)

  4. Failure of structures: can you see it coming (preprint)
    Hinke M. Osinga
    in Proceedings of the 2016 AEES Conference, Melbourne, Australian Earthquake Engineering Society, #368.

  5. Computing failure boundaries by continuation of a two-point boundary value problem (preprint)
    Hinke M. Osinga
    in A. Cunha, E. Caetano, P. Ribeiro and G. Müller (Eds.) Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014, Porto (2014) #MS10-263, pp. 1891–1897.

  6. How to crochet a space-filling pancake: the math, the art and what next (preprint)
    Bernd Krauskopf & Hinke M. Osinga &
    in G. Greenfield, G. Hart and R. Sarhangi (Eds.) Bridges Seoul Conference Proceedings, Tessellations Publishing, Phoenix, Arizona (2014), pp. 19–26.

  7. 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.

  8. 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, Tarquin Publications, pp. 9–14, 2008.

  9. 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, Tarquin Publications, pp. 255–260, 2006.

  10. 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.


  11.   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.


  12.   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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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 - 2007 LMS Popular lecture   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 DSWeb.

  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 DSWeb.


Preprints

  1. Computing parametrised large intersection sets of 1D invariant manifolds: a tool for blender detection
    Dana C'Julio, Bernd Krauskopf & Hinke M. Osinga
    Preprint University of Auckland, 2023.

  2. Characterising blenders via covering relations and cone conditions
    Maciej J. Capiński, Bernd Krauskopf, Hinke M. Osinga & Piotr Zgliczyński
    arXiv Preprint 2212.04861, 2023.

  3. Growing unstable manifolds of planar maps
    Bernd Krauskopf & Hinke M. Osinga
    IMA preprint 1517, 1997.

Copyright © 1996-2023 by Hinke Osinga
Last modified: Tue Sep 19 22:16:21 NZST 2023