Maciej (Martin) Krupa
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Peer reviewed publications

  1. S. Fernandez-Garcia, 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. (in press), 2015.   link

  2. M. Brøns, M. Desroches, M. Krupa, Mixed-mode oscillations due to a singular Hopf bifurcation in a forest pest model. Math. Popul. Stud. (in press), 2015.   link

  3. 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

  4. 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

  5. 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 ,   link

  6. 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

  7. 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

  8. 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).   link

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 79(S1), pp. 175-178 (2011).   link

  16. 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

  17. 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

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

  19. 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

  20. 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

  21. 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).   link

  22. 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

  23. M. Golubitsky and M. Krupa, Stability Computations for Nilpotent Hopf Bifurcations in Coupled Cell Systems. International Journal of Bifurcation and Chaos 17(8), pp. 2595-2603 (2007).   link

  24. 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

  25. 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

  26. 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

  27. 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

  29. 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

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

  31. 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

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

  33. 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

  34. M. Krupa and P. Szmolyan. Relaxation oscillations and canard explosion. JDE 174, 312-368 (2001).   link

  35. 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

  36. 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

  37. 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

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

  39. 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

  40. M. Krupa. Robust heteroclinic cycles (review article). J. of Nonl. Sci. 7(2), pp. 129-176 (1997).   link

  41. M. Krupa, B. Sandstede and P. Szmolyan. Fast and slow waves in the Fitzhugh-Nagumo equation. JDE 133(1), pp. 49-97 (1997).   link

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

  43. 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

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

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

  46. 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

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

  48. D.G. Aronson, S.A. van Gils and M. Krupa. Homoclinic twist bifurcations with Z2 symmetry. Journal of Nonlinear Science 4(1), pp. 195-219 (1994).   link

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

  50. 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

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

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

  53. 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

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

  55. 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).

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