Maciej (Martin) Krupa

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Peer reviewed publications

66. M. Desroches, S. Fernández-García and M. Krupa,
    Canards in a minimal piecewise-linear square-wave burster,
    Chaos , accepted, 2016.   LINK


65. M. Desroches, M. Krupa and S. Rodrigues,
    Spike-adding in parabolic bursters: the role of folded-saddle canards,
    Physica D 331 (1), 58-70, 2016.   LINK


64. S. Rodrigues*, M. Desroches*, M. Krupa*, J. M. Cortes, T. J. Sejnowski and A. B. Ali*,
    Time-coded neurotransmitter release at excitatory and inhibitory synapses (* joint first author),
    Proc. Natl. Acad. Sci. USA 113 (8), E1108-E1115, 2016.   LINK


63. E. Köksal-Ersöz, M. Desroches, M. Krupa and F. Clément,
    Canard-mediated (de)synchronisation in coupled phantom bursters,
    SIAM J. Appl. Dyn. Syst. 15 (1), 580-608, 2016.   LINK


62. J. Burke, M. Desroches, A. Granados, T. J. Kaper, M. Krupa and T. Vo,
    From canards of folded singularities to torus canards in a forced van der Pol equation,
    J. Nonlinear Sci. 26 (2), 405-451, 2016.   LINK


61. P. Chossat and M. Krupa,
    Heteroclinic cycles in Hopfield networks,
    J. Nonlinear Sci., in press, 2015.   LINK


60. S. Fernández-García, M. Desroches, M. Krupa and A. E. Teruel,
    Canard solutions in planar piecewise linear systems with three zones,
    Dynam. Syst. 31 (2), 173-197, 2015.   LINK


59. M. Krupa and J. Touboul,
    Canard explosion in delay differential equations,
    J. Dynam. Diff. Eq., in press, 2015.   LINK


58. M. Krupa and J. Touboul,
    Complex oscillations in the delayed FitzHugh-Nagumo equation,
    J. Nonlinear Sci. 26 (1), 43-81, 2015.   LINK


57. J. Touboul, M. Krupa and M. Desroches,
    Noise-induced canards and mixed-mode oscillations in large-scale stochastic networks,
    SIAM J. Appl. Math. 75 (5), 2024-2049, 2015.   LINK


56. E. Benoît, M. Brøns, M. Desroches and M. Krupa,
    Extending the zero-derivative principle for slow-fast dynamical systems,
    Z. Angew. Math. Phys. (ZAMP) 66 (5), 2255-2270, 2015.   LINK


55. S. Fernáandez-García, M. Desroches, M. Krupa and F. Clément,
    A Multiple Time Scale Coupling of Piecewise Linear Oscillators. Application to a Neuroendocrine System,
    SIAM J. Appl. Dyn. Syst. 14 (2), 643-673, 2015.   LINK


54. M. Brøns, M. Desroches, M. Krupa,
    Mixed-mode oscillations due to a singular Hopf bifurcation in a forest pest model,
    Math. Popul. Stud. 22 (2), 71-79, 2015.   LINK


53. A. Granados and M. Krupa,
    Firing-rate, symbolic dynamics and frequency dependence in periodically driven spiking models: a piecewise-smooth approach,
    Nonlinearity 28, 1163-1192, 2015.   LINK


52. A. Granados, M. Krupa and F. Clément,
    Border collision bifurcations of stroboscopic maps in periodically driven spiking models,
    SIAM J. Appl. Dyn. Syst. 13 (4), 1387-1416, 2014.   LINK


51. S. Gielen, M. Krupa and B. Gutkin,
    Adaptation and shunting inhibition leads to pyramidal/interneuron gamma with sparse firing of interneurons,
    J. Comput. Neurosci. 37 (2), 357-376 ,   PDF   LINK


50. M. Krupa, B. Ambrosio and M. A. Aziz-Alaoui,
    Weakly coupled two fast- two slow systems, folded node and mixed-mode oscillations,
    Nonlinearity 27(7), pp. 1555-1575 , 2014.   LINK


49. H. W. Broer, T. J. Kaper and M. Krupa,
    Geometric Desingularization of a Cusp Singularity in Slow–Fast Systems with Applications to Zeeman’s Examples,
    J. Dyn. Diff. Equat. 25(4), pp. 925-958, 2013.   LINK


48. M. Desroches, T. J. Kaper and M. Krupa,
    Mixed-mode bursting oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster,
    Chaos 23(4), pp. 046106 (2013).   PDF  LINK


47. L. Fontolan, M. Krupa, A. Hyafil and B. Gutkin,
    Analytical insights on theta-gamma coupled neural oscillators,
    The Journal of Mathematical Neuroscience 3:16 (2013).   LINK


46. M. Krupa, A. Vidal and F. Clément,
    A Network Model of the Periodic Synchronization Process in the Dynamics of Calcium Concentration in GnRH Neurons,
    The Journal of Mathematical Neuroscience 3:4 (2013).   LINK


45. M. Desroches, M. Krupa and S. Rodrigues,
    Canards, inflection and excitability threshold in neuronal models,
    J. Math. Biol. 67(4), pp. 989-1017 (2013).   LINK


44. M. Krupa, A. Vidal, M. Desroches and F. Clément,
    Mixed-Mode Oscillations in a Multiple Time Scale Phantom Bursting System,
    SIAM J. Appl. Dyn. Syst. 11(4), pp. 1458-1498 (2012).   LINK


43. M. Dipoppa, M. Krupa, A. Torcini and B. S. Gutkin,
    Splay states in excitatory finite size neural networks subjected to pulses of finite amplitude and duration,
    SIAM J. Appl. Dyn. Syst. 11(3), pp. 864-894 (2012).   LINK


42. H. G. E Meijer, M. Krupa, H. Cagnan, M. A. J Lourens, T. Heida, H. C. F Martens, L. J. Bour and S. A. Van Gils,
    From Parkinsonian thalamic activity to restoring thalamic relay using deep brain stimulation: new insights from computational modeling,
    J. Neur. Eng. 8(6), pp. 066005 (2011).   LINK


41. M. Krupa, M. Schagerl, A. Steindl, W. Steiner and H. Troger,
    A Comparison of Various Methods for the Stability Analysis of the Relative Equilibria of a Rotating Pendulum,
    Z. Angew. Math. Mech. (ZAMM) 79(S1), pp. 175-178 (2011).   LINK


40. J. Jalics, M. Krupa and H. G. Rotstein,
    Mixed-mode oscillations in a three time-scale system of ODEs motivated by a neuronal model,
    Dynamical Systems 25(4), pp. 445-482 (2010).   LINK


39. M. Krupa, S. Gielen and M. Zeitler,
    Gamma oscillations as a mechanism for selective information transmission,
    Biological Cybernetics 103(2), pp. 151-165 (2010).   LINK


38. M. Krupa and M. Wechselberger,
    Local analysis near a folded saddle-node singularity,
    J. Diff. Eq. 248(12), pp. 2841-2888 (2010).   LINK


37. C. Börgers, S. Gielen and M. Krupa,
    The response of a population of classical Hodgkin-Huxley neurons to an inhibitory pulse,
    J. Comput. Neurosci. 28(3), pp. 509-526 (2010).   LINK


36. H. Cagnan, H. Meijer, S. van Gils, M. Krupa, T. Heida, M. Rudolph, W. Wadman and H. Martens,
    Frequency-selectivity of a thalamocortical relay neuron during Parkinson's disease and deep brain stimulation: a computational study,
    Eur. J. Neurosci. 30(7), pp. 1306-1317 (2009).   LINK


35. M. Krupa, N. Popovic and N. Kopell,
    Mixed-mode oscillations in three timescale systems--a prototypical example,
    SIAM J. Appl. Dyn. Syst. 7(2), pp. 361-420 (2008).   PDF   LINK


34. M. Krupa, N. Popovic, N. Kopell and H. G. Rotstein,
    Mixed-mode oscillations in a three timescale model of a dopaminergic neuron,
    Chaos 18(2), pp. 015106 (2008).   LINK


33. M. Golubitsky and M. Krupa,
    Stability Computations for Nilpotent Hopf Bifurcations in Coupled Cell Systems,
    Int. J. Bifurcation and Chaos 17(8), pp. 2595-2603 (2007).   LINK


32. M. Brøns, M. Krupa and M. Wechselberger,
    Mixed mode oscillations due to the generalized canard phenomenon,
    Fields Inst. Comm. 49, pp. 39-63 (2006).   LINK


31. M.Krupa, W. Poth, M. Schagerl, A. Steindl, W. Steiner, H. Troger, G. Wiedermann,
    Modelling, dynamics and control of tethered satellite systems,
    Nonlinear Dynam. 43 73-96 (2006).   LINK


30. E. Barany and M. Krupa,
    Stability of multiple access network control schemes with carrier sensing and exponential backoff,
    Physica A 363 573-590 (2006).   LINK


29. S.A. van Gils, M. Krupa and P. Szmolyan,
    Asymptotic expansions using blow-up,
    ZAMP 56, 369-397 (2005).   LINK


28. M. Krupa, I. S. Melbourne,
    Asymptotic stability of heteroclinic cycles in systems with symmetry, II,
    Proc. Roy. Soc. Edinburgh A 134A, 1177-1197 (2004).   LINK


27. E. Barany and M. Krupa,
    Emergence of critical rates in multiple access network control schemes,
    Proceedings of the 42nd IEEE Conference on Decision and Control, 1592-1597, Maui, HI, December (2003).   LINK


26. M. Krupa and P. Szmolyan,
    Extending slow manifolds near transcritical and pitchfork singularities,
    Nonlinearity 14(6), pp. 1473-1491 (2001).   LINK


25. M. Krupa, M. Schagerl, A. Steindl, P. Szmolyan and H. Troger,
    Relative equilibria of tethered satellite systems and their stability for very stiff tethers,
    Dyn. Syst. 16, 253--278 (2001).   LINK


24. M. Krupa, A. Steindl, and H. Troger,
    Stability of Relative Equilibria. Part II: Dumbell Satellites,
    Meccanica 35(4), pp. 353-371 (2001).   LINK


23. M. Krupa, M. Schagerl, A. Steindl, and H. Troger,
    Stability of Relative Equilibria. Part I: Comparison of four methods (expository article),
    Meccanica 35(4), pp. 325-351 (2001).   LINK


22. M. Krupa and P. Szmolyan,
    Relaxation oscillations and canard explosion,
    J. Differential Equations 174, 312-368 (2001).   LINK


21. M. Krupa and P. Szmolyan,
    Extending geometric singular perturbation theory to non-hyperbolic points -- fold and canard points in two dimensions,
    SIAM. J. of Math. Anal. 33(2), pp. 286-314 (2001).   LINK


20. M. Krupa and P. Szmolyan,
    Geometric analysis of the singularly perturbed planar fold, In: Multiple-Time-Scale Dynamical Systems,
    IMA Volume 122 Editors: Christopher K.R.T. Jones and Alexander Khibnik, 89-116 Springer, New York (2001).   LINK


19. S. A. van Gils, M. Krupa and V. Tchistiakov,
    Homoclinic twist bifurcation in a system of two coupled oscillators,
    J. Dyn. Diff. Equat. 12(4), pp. 733-806 (2000).   LINK


18. B. Katzengruber, M. Krupa and P. Szmolyan,
    Bifurcation of travelling waves in extrinsic semiconductors,
    Physica D 144(1-2), pp. 1-19 (2000).   LINK


17. P. Chossat, M. Krupa, I. Melbourne and A. Scheel,
    Magnetic dynamos in rotating convection - a dynamical systems approach,
    Dyn. Cont. Discr. Impulsive Syst. 5, pp. 327-340 (1999).    ps


16. M. Krupa,
    Robust heteroclinic cycles (review article),
    J. Nonlinear Sci. 7(2), pp. 129-176 (1997).   LINK


15. M. Krupa, B. Sandstede and P. Szmolyan,
    Fast and slow waves in the Fitzhugh-Nagumo equation,
    J. Differential Equations 133(1), pp. 49-97 (1997).   LINK


14. P. Chossat, M. Krupa, I. Melbourne and A. Scheel,
    Transverse bifurcations of homoclinic cycles,
    Physica D 100(1-2), pp. 85-100 (1997).   LINK


13. M. Krupa, M. Schagerl, A. Steindl and H. Troger,
    Relative equilibria of tethered satellite systems and their stability, Proceedings ICIAM 95,
    ZAMM    Special Issue 4, 325-344 (1996).   LINK


12. D.G. Aronson, M. Krupa and P.B. Ashwin,
    Semirotors in Josephson junctions equations,
    J. Nonlinear Sci. 6(1), pp. 85-103 (1996).   LINK


11. M. Krupa and I. Melbourne,
    Nonasymptotically stable attractors in O(2) mode interactions,
    Fields Institute Communications 4, 219-233 (1995).   LINK


10. M. Krupa and I. Melbourne. Asymptotic stability of heteroclinic cycles in systems with symmetry, Ergodic Theory Dyn. Syst., 15(01), pp. 121-147 (1995).   LINK


9. A. Homburg, H. Kokubu and M. Krupa,
   The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit,
   Ergodic Theory Dyn. Syst. 14(04), pp. 667-693, (1994).   LINK


8. D.G. Aronson, S.A. van Gils and M. Krupa,
   Homoclinic twist bifurcations with Z₂ symmetry,
   J. Nonlinear Sci. 4(1), pp. 195-219 (1994).   LINK


7. M. Krupa and M. Roberts,
   Symmetry breaking and symmetry locking in equivariant circle maps,
   Physica D 57(3-4), pp. 417-435 (1992).   LINK


6. D.G. Aronson, S.A. van Gils and M. Krupa,
   The homoclinic twist bifurcation point, In: Bifurcation and Symmetry, edited by E. Allgower, K. Böhmer and M. Golubitsky,
   International Series of Numerical Mathematics vol. 104, Birkhäuser, Basel, pp. 11-22 (1992).   LINK


5. D.G. Aronson, M. Golubitsky and M. Krupa,
   Coupled arrays of Josephson junctions and bifurcations of maps with S_N symmetry,
   Nonlinearity 4(3), pp. 861-902 (1991).   LINK


4. M. Golubitsky, M. Krupa and C. Lim,
   Time-reversibility and particle sedimentation,
   SIAM J. Appl. Math. 51(1), pp. 49-72 (1991).   LINK


3. S.A. van Gils, M. Krupa and W.F. Langford,
   Hopf bifurcation with non-semisimple 1:1 resonance,
   Nonlinearity 3(3), pp. 825-850 (1990).   LINK


2. M. Krupa,
   Bifurcations of relative equilibria,
   SIAM J. Math. Anal. 21(6), pp. 1453-1486 (1990).   LINK


1. A. Vanderbauwhede, M. Krupa and M. Golubitsky,
   Secondary bifurcations in symmetric systems, In: Differential Equations (C. M. Dafermos, G. Ladas and G. Papanicolaou, eds.),
   Lecture Notes in Pure and Applied Mathematics vol. 118, Marcel Dekker, New York, pp. 709-716 (1989).

Preprints

• M. Desroches, M. Krupa, S. Rodrigues,
  Spike-adding mechanism in parabolic bursters: the role of folded-saddle canards.
  Submitted for publication.   HAL


• S. Fernández-García, M. Desroches and M. Krupa,
  Canards and spike-adding transitions in a minimal piecewise-linear Hindmarsh-Rose square-wave burster.
  Submitted for publication.


• D. Avitabile, M. Desroches, E. Knobloch and M. Krupa.
  Ducks in space.
  Under revision.


• A Granados, L Alsedà, M Krupa.
  Period adding and incrementing gluing bifurcations in one-dimensional piecewise-smooth maps: theory and applications.
  Under revision.   ARXIV


• S. Fernández-García, M. Krupa and F. Clément. Mixed-mode oscillations in a piecewise-linear system with multiple time scale coupling.
  Under revision.