Peer reviewed publications
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- M. Krupa and M. Wechselberger, Local analysis near a
folded saddle-node singularity. J. Diff. Eq. 248(12),
pp. 2841-2888 (2010). link
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- S.A. van Gils, M. Krupa and P. Szmolyan. Asymptotic
expansions using blow-up. ZAMP 56, 369-397 (2005).
link
- 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
- 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
- M. Krupa and P. Szmolyan, Extending slow manifolds near
transcritical and pitchfork singularities. Nonlinearity
14(6), pp. 1473-1491 (2001). link
- 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
- M. Krupa, A. Steindl, and H. Troger. Stability of
Relative Equilibria. Part II: Dumbell Satellites. Meccanica
35(4), pp. 353-371 (2001). link
- 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
- M. Krupa and P. Szmolyan. Relaxation oscillations and
canard explosion. JDE 174, 312-368 (2001).
link
- 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
- 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
- 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
- B. Katzengruber, M. Krupa and P. Szmolyan. Bifurcation
of travelling waves in extrinsic semiconductors. Physica D
144(1-2), pp. 1-19 (2000). link
- 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
- M. Krupa. Robust heteroclinic cycles (review article).
J. of Nonl. Sci. 7(2), pp. 129-176 (1997).
link
- M. Krupa, B. Sandstede and P. Szmolyan. Fast and slow
waves in the Fitzhugh-Nagumo equation. JDE 133(1),
pp. 49-97 (1997). link
- P. Chossat, M. Krupa, I. Melbourne and
A. Scheel. Transverse bifurcations of homoclinic cycles. Physica
D 100(1-2), pp. 85-100 (1997). link
- 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
- D.G. Aronson, M. Krupa and P.B. Ashwin. Semirotors in
Josephson junctions equations. J. Nonl. Sci. 6(1),
pp. 85-103 (1996). link
- M. Krupa and I. Melbourne. Nonasymptotically stable
attractors in O(2) mode interactions. Fields Institute
Communications 4, 219-233 (1995). link
- 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
- 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
- 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
- M. Krupa and M. Roberts. Symmetry breaking and symmetry
locking in equivariant circle maps. Physica D 57(3-4),
pp. 417-435 (1992). link
- 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
- 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
- M. Golubitsky, M. Krupa and C. Lim. Time-reversibility
and particle sedimentation. SIAM J. Appl. Math. 51(1),
pp. 49-72 (1991). link
- 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
- M. Krupa. Bifurcations of relative equilibria. SIAM
J. Math. Anal. 21(6), pp. 1453-1486 (1990). link
- 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
- A Granados, L Alsedà, M Krupa.
Period adding and incrementing gluing bifurcations in one-dimensional piecewise-smooth maps: theory and applications, submitted.
arxiv
- S. Fernandez-Garcia, M. Desroches, M. Krupa and A. Teruel,
Canard solutions in planar piecewise linear systems with three zones, submitted.
- M. Desroches, M. Krupa, S. Rodrigues.
Spike-adding mechanism in parabolic bursters: the role of folded-saddle and jump-on canards. submitted.
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