book
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M. Wechselberger,
Geometric singular perturbation theory beyond the standard form,
to appear in Frontiers in Applied Dynamics: Reviews and Tutorials (2019),
book chapters
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R. Bertram, J. Tabak, W. Teka, T. Vo, M. Wechselberger,
Geometric singular perturbation analysis of bursting oscillations in pituitary cells,
in Mathematical Analysis of Complex Cellular Activity,
Frontiers in Applied Dynamics: Reviews and Tutorials 1 (2015), 1-52, Springer. DOI -
M. Wechselberger, J. Mitry, J. Rinzel,
Canard theory and excitability,
in Nonautonomous Dynamical Systems in the Life Sciences, P. Kloeden, C. Poetzsche (eds.),
Lecture Notes in Mathematics 2102 (2013), 89-132. DOI -
M. Brons, M. Krupa, M. Wechselberger,
Mixed Mode Oscillations Due to the Generalized Canard Phenomenon,
Fields Institute Communications 49 (2006), 39-63. PDF
journal articles
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J. Mitry, M. Wechselberger,
Folded saddles & faux canards,
SIAM Journal on Applied Dynamical Systems 16 (2017), 546-596. DOI -
P. Carter, E. Knobloch, M. Wechselberger,
Transonic canards and stellar wind,
Nonlinearity 30 (2017), 1006-1033. DOI -
M. Hayes, T. Kaper, P. Szmolyan, M. Wechselberger,
Geometric desingularization of degenerate singularities in the presence of rotation: a new proof of known results for slow passage through Hopf bifurcation,
Indagationes Mathematicae 27 (2016), 1184-1203. DOI -
S. Boie, V. Kirk, J. Sneyd, M. Wechselberger,
Effects of quasi-steady state reduction on biophysical models with oscillations,
Journal of Theoretical Biology 393 (2016), 16-31. DOI -
K.-L. Roberts, J. Rubin, M. Wechselberger,
Averaging, foIded singularities and torus canards: explaining transitions between bursting and spiking in a coupled neuron model,
SIAM Journal on Applied Dynamical Systems 14 (2015), 1808-1844. DOI -
T. Vo, M. Wechselberger,
Canards of Folded Saddle-Node Type I,
SIAM Journal on Mathematical Analysis 47 (2015), 3235-3283. DOI -
G. Ullah, Y. Wei, M. Dahlem, M. Wechselberger, S. Schiff,
The role of cell volume in the dynamics of seizure, spreading depression, and anoxic depolarization
PLOS Computational Biology 11 (2015), e1004414. DOI -
P. de Maesschalck, M. Wechselberger,
Neural excitability and singular bifurcations,
Journal of Mathematical Neuroscience 5 (2015), 16. DOI -
K. Harley, P. van Heijster, R. Marangell, G. Pettet, M. Wechselberger,
Numerical computation of an Evans function for travelling waves,
Mathematical Biosciences 266 (2015), 36-51. DOI
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A. Roberts, E. Widiasih, M. Wechselberger, C.K.R.T. Jones
Mixed mode oscillations in a conceptual climate model,
Physica D 292-293 (2015), 70-83. DOI -
K. Harley, P. van Heijster, R. Marangell, G. Pettet, M. Wechselberger,
Novel solutions for a model of wound healing angiogenesis,
Nonlinearity 27 (2014), 2975-3003. DOI -
X.B. Lin, M. Wechselberger,
Transonic evaporation waves in a spherically symmetric nozzle,
SIAM Journal on Mathematical Analysis 46 (2014), 1472-1504. DOI -
T. Vo, J. Tabak, R. Bertram, M. Wechselberger,
A geometric understanding how fast activating potassium channels promote bursting in pituitary cells,
J. Comp. Neurosci. 36 (2014), 259-278. DOI -
K. Harley, P. van Heijster, R. Marangell, G. Pettet, M. Wechselberger,
Existence of travelling wave solutions for a model of tumour invasion,
SIAM Journal on Applied Dynamical Systems 13 (2014), 366-396. DOI -
J. Mitry, M. McCarthy, N. Kopell, M. Wechselberger,
Excitable neurons, firing threshold manifolds and canards,
Journal of Mathematical Neuroscience 3 (2013), 12. DOI -
T. Vo, R. Bertram, M. Wechselberger,
Multiple geometric viewpoints of mixed mode dynamics associated with pseudo-plateau bursting,
SIAM J. Appl. Dyn. Syst. 12 (2013), 789-830. DOI -
M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. Osinga, M. Wechselberger,
Mixed-mode oscillatons with multiple time-scales,
SIAM Review 54 (2012), 211-288. DOI -
T. Vo, R. Bertram, M. Wechselberger,
Bifurcations of canard-induced mixed mode oscillations in a pituitary lactotroph model,
Discrete and Continuous Dynamical Systems - A 32 (2012), 2879-2912. DOI -
M. Wechselberger,
A propos de canards (apropos canards),
Transactions of the American Mathematical Society 364 (2012), 3289-3309. DOI -
W.Teka, J. Tabak, T. Vo, M. Wechselberger, R. Bertram,
The dynamics underlying pseudo-plateau bursting in a pituitary cell model,
Journal of Mathematical Neuroscience 1 (2011), 12. DOI -
W. Zhang, V. Kirk, J. Sneyd and M. Wechselberger,
Changes in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescales,
Journal of Mathematical Neuroscience 1 (2011), 9. DOI -
E. Harvey, V. Kirk, J. Sneyd, M. Wechselberger,
Multiple time scales, mixed-mode oscillations and canards in models of intracellular calcium dynamics,
Journal of Nonlinear Science 21 (2011), 639-683. DOI
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E. Harvey, V. Kirk, H. Osinga, J. Sneyd, M. Wechselberger,
Understanding anomalous delays in a model of intracellular calcium dynamics,
Chaos 20 (2010), 045104. DOI -
M. Wechselberger, G. Pettet,
Folds, canards and shocks in advection-reaction-diffusion models,
Nonlinearity 23 (2010), 1949-1969. DOI -
T. Vo, R. Bertram, J. Tabak, M. Wechselberger,
Mixed mode oscillations as a mechanism for pseudo-plateau bursting,
J. Comp. Neurosci. 28 (2010), 443-458. DOI -
M. Krupa, M. Wechselberger,
Local analysis near a folded saddle-node singularity,
J. Differential Equations 248 (2010), 2841-2888. DOI -
M. Wechselberger, W. Weckesser,
Homoclinic clusters and chaos associated with a folded node in a stellate cell model,
DCDS-S 2 (2009), 829-850. DOI -
M. Wechselberger, W. Weckesser,
Bifurcations of mixed-mode oscillations in a stellate cell model,
Physica D 238 (2009), 1598-1614. DOI -
B. Ermentrout, M. Wechselberger,
Canards, clusters and synchronization in a weakly coupled interneuron model,
SIAM J. Appl. Dyn. Syst. 8 (2009), 253-278. DOI -
M. Beck, C.K.R.T. Jones, D. Schaeffer, M. Wechselberger,
Electrical waves in a one-dimensional model of cardiac tissue,
SIAM J. Appl. Dyn. Syst. 7 (2008), 1558-1581. DOI -
H. Rotstein, M. Wechselberger, N. Kopell,
Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model,
SIAM J. Appl. Dyn. Syst. 7 (2008), 1582-1611. DOI -
J. Rubin, M. Wechselberger,
The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales,
Chaos 18 (2008), 015105. DOI -
J. Rubin, M. Wechselberger,
Giant Squid - Hidden Canard: the 3D Geometry of the Hodgkin Huxley Model,
Biological Cybernetics 97 (2007), 5-32. DOI -
M. Wechselberger,
Canards,
Scholarpedia 2 (2007), 1356. DOI -
M. Wechselberger, C. Wright, G. Bishop, J. Boulant,
Ionic channels and conductance-based models for hypothalamic neuronal sensitivity,
Am J Physiol Regulatory Integrative Comp Physiol 291 (2006), 518-529. DOI -
J. Guckenheimer, M. Wechselberger, L.-S. Young,
Chaotic Attractors of Relaxation Oscillators,
Nonlinearity 19 (2006), 701-720. DOI -
J. Best, A. Borisyuk, J. Rubin, D. Terman, M. Wechselberger,
The Dynamic Range of Bursting in a Model Respiratory Pacemaker Network,
SIAM J. Applied Dynamical Systems 4 (2005), 1107-1139. DOI -
M. Wechselberger,
Existence and Bifurcation of Canards in R^3 in the case of a Folded Node,
SIAM J. Applied Dynamical Systems 4 (2005), 101-139. DOI -
P. Szmolyan, M. Wechselberger,
Relaxation Oscillations in R^3,
J Differential Equations 200 (2004), 69-104. DOI -
M. Wechselberger,
Extending Melnikov-theory to invariant manifolds on non-compact domains,
Dynamical Systems: An International Journal 17 (2002), 215-233. DOI -
P. Szmolyan, M. Wechselberger,
Canards in R^3,
J Differential Equations 177 (2001), 419-453. DOI
proceedings
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M. Wechselberger,
Poincare Maps for Relaxation Oscillations in R^3 - Invariant Manifolds, Canards and Turning Points,
Proceedings of "Equadiff 03", Hasselt, Belgium (2005).
