(Department of Mathematics, University of Auckland) Marsden Fund (2020-2023): `Modelling calcium dynamics in living animals: multiple time and space scales in theory and practice.', V. Kirk, J. Sneyd, M. Graff, M. Wechselberger. Marsden Fund (2016-2018): `Surprisingly slow dynamics in calcium models: where are the slow time scales', V. Kirk, J. Sneyd, H. Osinga, M. Wechselberger. Marsden Fund (2012-2014): `Applications of multiscale excitable systems to calcium dynamics and neuroscience', V. Kirk, J. Sneyd, H. Osinga, M. Wechselberger. Marsden Fund (2008-2011): `Designing experiments using mathematics: nonlinear dynamics and calcium oscillations', V. Kirk, J. Sneyd, H. Osinga, M. Wechselberger.

Current research students

Project title	Research student
Mathematical and Computational Approaches to Optimising Immunotherapy to Treat Cancer	Georgio HAWI
Nonstandard geometric singular perturbation theory methods of model reductions for biochemical reaction networks with multiple time-scales	Timothy LAPUZ

Selected publications

Geometric Singular Perturbation Theory Beyond the Standard Form

(Springer, 2020)

Publications

By Type

Expand all

Books

Wechselberger, M. (2020). Geometric Singular Perturbation Theory Beyond the Standard Form. Cham: Springer. [More Information]

Book Chapters

Bertram, R., Tabak, J., Teka, W., Vo, T., Wechselberger, M. (2015). Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells. In R. Bertram, J. Tabak, W. Teka, T. Vo, M. Wechselberger, V. Kirk, J. Sneyd (Eds.), Mathematical Analysis of Complex Cellular Activity, (pp. 1-52). Cham: Springer. [More Information]
Wechselberger, M., Mitry, J., Rinzel, J. (2013). Canard Theory and Excitability. In Peter E Kloeden, Christian Potzsche (Eds.), Nonautonomous Dynamical Systems in the Life Sciences, (pp. 89-132). Cham, Switzerland: Springer. [More Information]

Journals

Miller, T., Tam, A., Marangell, R., Wechselberger, M., Bradshaw- Hajek, B. (2025). Shock selection in reaction–diffusion equations with partially negative diffusivity using nonlinear regularisation. Physica D: Nonlinear Phenomena, 474, 134561-1-134561-14. [More Information]
Bradshaw-Hajek, B., Lizarraga, I., Marangell, R., Wechselberger, M. (2024). A Geometric Singular Perturbation Analysis of Shock Selection Rules in Composite Regularized Reaction-Nonlinear Diffusion Models. SIAM Journal on Applied Dynamical Systems, 23(3), 2099-2137. [More Information]
Miller, T., Tam, A., Marangell, R., Wechselberger, M., Bradshaw-Hajek, B. (2024). Analytic shock-fronted solutions to a reaction–diffusion equation with negative diffusivity. Studies in Applied Mathematics, 153(Open Access), e12685-1-e12685-23. [More Information]
Abelson, D., Di Michiel, J., Frater, C., Pearson, M., Russo, R., Wechselberger, M., Cottee, A., Morgan, L. (2024). Mucus clears from the trachea in a helix: a new twist to understanding airway diseases. Thorax, 79(7), 607-614. [More Information]
Hester, E., Vasil, G., Wechselberger, M. (2022). On the stability of shocks in isothermal black hole accretion discs. Monthly Notices of the Royal Astronomical Society, 512(4), 5771-5781. [More Information]
Jelbart, S., Pages, N., Kirk, V., Sneyd, J., Wechselberger, M. (2022). Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics. SIAM Journal on Applied Dynamical Systems, 21 (Open Access)(2), 982-1029. [More Information]
Jelbart, S., Kristiansen, K., Szmolyan, P., Wechselberger, M. (2022). Singularly Perturbed Oscillators with Exponential Nonlinearities. Journal of Dynamics and Differential Equations, 34(3), 1823-1875. [More Information]
Lizarraga, I., Rink, B., Wechselberger, M. (2021). Multiple timescales and the parametrisation method in geometric singular perturbation theory. Nonlinearity, 34, 4163-4201. [More Information]
Li, Y., van Heter, P., Simpson, M., Wechselberger, M. (2021). Shock-fronted travelling waves in a reaction–diffusion model with nonlinear forward–backward–forward diffusion. Physica D: Nonlinear Phenomena, 423(Open Access), 132916 - 1-132916 - 14. [More Information]
Jelbart, S., Kristiansen, K., Wechselberger, M. (2021). Singularly perturbed boundary-equilibrium bifurcations. Nonlinearity, 34(11), 7371-7414. [More Information]
Jelbart, S., Kristiansen, K., Wechselberger, M. (2021). Singularly perturbed boundary-focus bifurcations. Journal of Differential Equations, 296, 412-492. [More Information]
Harley, K., van Heijster, P., Marangell, R., Pettet, G., Roberts, T., Wechselberger, M. (2020). (In)stability of travelling waves in a model of haptotaxis. SIAM Journal on Applied Mathematics, 80(4), 1629-1653. [More Information]
Lizarraga, I., Wechselberger, M. (2020). Computational Singular Perturbation Method for Nonstandard Slow-Fast Systems. SIAM Journal on Applied Dynamical Systems, 19(2), 994-1028. [More Information]
Avitabile, D., Desroches, M., Veltz, R., Wechselberger, M. (2020). Local Theory for Spatio-Temporal Canards and Delayed Bifurcations. SIAM Journal On Mathematical Analysis, 52(6), 5703-5747. [More Information]
Lizarraga, I., Marangell, R., Wechselberger, M. (2020). Slow Unfoldings of Contact Singularities in Singularly Perturbed Systems Beyond the Standard Form. Journal of Nonlinear Science, 30, 3161-3198. [More Information]
Jelbart, S., Wechselberger, M. (2020). Two-stroke relaxation oscillators. Nonlinearity, 33(5), 2364-2408. [More Information]
Mitry, J., Wechselberger, M. (2017). Folded Saddles and Faux Canards. SIAM Journal on Applied Dynamical Systems, 16(1), 546-596. [More Information]
Carter, P., Knobloch, E., Wechselberger, M. (2017). Transonic canards and stellar wind. Nonlinearity, 30(3), 1006-1033. [More Information]
Boie, S., Kirk, V., Sneyd, J., Wechselberger, M. (2016). Effects of quasi-steady state reduction on biophysical models with oscillations. Journal of Theoretical Biology, 393, 16-31. [More Information]
Hayes, M., Kaper, T., Szmolyan, P., Wechselberger, M. (2016). Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations. Indagationes Mathematicae, 27(5), 1184-1203. [More Information]
Roberts, K., Rubin, J., Wechselberger, M. (2015). Averaging, foIded singularities and torus canards: explaining transitions between bursting and spiking in a coupled neuron model. SIAM Journal on Applied Dynamical Systems, 14(4), 1808-1844. [More Information]
Vo, T., Wechselberger, M. (2015). Canards of folded saddle-node type I. SIAM Journal On Mathematical Analysis, 47(4), 3235-3283. [More Information]
Roberts, A., Widiasih, E., Wechselberger, M., Jones, C. (2015). Mixed mode oscillations in a conceptual climate model. Physica D: Nonlinear Phenomena, 292-293, 70-83. [More Information]
De Maesschalck, P., Wechselberger, M. (2015). Neural Excitability and Singular Bifurcations. Journal of Mathematical Neuroscience, 5(16), 1-32. [More Information]
Harley, K., van Heijster, P., Marangell, R., Pettet, G., Wechselberger, M. (2015). Numerical computation of an Evans function for travelling waves. Mathematical Biosciences, 266, 36-51. [More Information]
Ullah, G., Wei, Y., Dahlem, M., Wechselberger, M., Schiff, S. (2015). The Role of Cell Volume in the Dynamics of Seizure, Spreading Depression, and Anoxic Depolarization. PLoS Computational Biology, 11(8), 1-25. [More Information]
Vo, T., Tabak, J., Bertram, R., Wechselberger, M. (2014). A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells. Journal of Computational Neuroscience, 36(2), 259-278. [More Information]
Harley, K., van Heijster, P., Marangell, R., Pettet, G., Wechselberger, M. (2014). Existence of Traveling Wave Solutions for a Model of Tumor Invasion. SIAM Journal on Applied Dynamical Systems, 13(1), 366-396. [More Information]
Harley, K., van Heijster, P., Marangell, R., Pettet, G., Wechselberger, M. (2014). Novel solutions for a model of wound healing angiogenesis. Nonlinearity, 27(12), 2975-3003. [More Information]
Lin, X., Wechselberger, M. (2014). Transonic evaporation waves in a spherically symmetric nozzle. SIAM Journal On Mathematical Analysis, 46(2), 1472-1504. [More Information]
Vo, T., Tabak, J., Bertram, R., Wechselberger, M. (2013). Canard- and Hopf-induced bursting in pituitary cells. Gazette of the Australian Mathematical Society, 40(3), 199-201.
Mitry, J., McCarthy, M., Kopell, N., Wechselberger, M. (2013). Excitable Neurons, Firing Threshold Manifolds and Canards. Journal of Mathematical Neuroscience, 3(12), 1-32. [More Information]
Vo, T., Bertram, R., Wechselberger, M. (2013). Multiple geometric viewpoints of mixed mode dynamics associated with pseudo-plateau bursting. SIAM Journal on Applied Dynamical Systems, 12(2), 789-830. [More Information]
Wechselberger, M. (2012). A Propos de Canards. Transactions of the American Mathematical Society, 364(6), 3289-3309. [More Information]
Vo, T., Bertram, R., Wechselberger, M. (2012). Bifurcations of canard-induced mixed mode oscillations in a pituitary Lactotroph model. Discrete and Continuous Dynamical Systems - Series A, 32(8), 2879-2912. [More Information]
Desroches, M., Guckenheimer, J., Krauskopf, B., Kuehn, C., Osinga, H., Wechselberger, M. (2012). Mixed-Mode Oscillations with Multiple Time Scales. SIAM Review, 54(2), 211-288. [More Information]
Zhang, W., Kirk, V., Sneyd, J., Wechselberger, M. (2011). Changes in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescales. Journal of Mathematical Neuroscience, 1(9), 1-22. [More Information]
Harvey, E., Kirk, V., Wechselberger, M., Sneyd, J. (2011). Multiple Timescales, Mixed Mode Oscillations and Canards in Models of Intracellular Calcium Dynamics. Journal of Nonlinear Science, 21, 639-683. [More Information]
Teka, W., Tabak, J., Vo, T., Wechselberger, M., Bertram, R. (2011). The dynamics underlying pseudo-plateau bursting in a pituitary cell model. Journal of Mathematical Neuroscience, 1(12), 1-23. [More Information]
Wechselberger, M., Pettet, G. (2010). Folds, canards and shocks in advection-reaction-diffusion models. Nonlinearity, 23, 1949-1969. [More Information]
Krupa, M., Wechselberger, M. (2010). Local analysis near a folded saddle-node singularity. Journal of Differential Equations, 248(12), 2841-2888. [More Information]
Vo, T., Bertram, R., Tabak, J., Wechselberger, M. (2010). Mixed mode oscillations as a mechanism for pseudo-plateau bursting. Journal of Computational Neuroscience, 28(3), 443-458. [More Information]
Harvey, E., Kirk, V., Osinga, H., Sneyd, J., Wechselberger, M. (2010). Understanding anomalous delays in a model of intracellular calcium dynamics. Chaos, 20(4), 045104-1-045104-19. [More Information]
Wechselberger, M., Weckesser, W. (2009). Bifurcations of mixed-mode oscillations in a stellate cell model. Physica D: Nonlinear Phenomena, 238(16), 1598-1614. [More Information]
Ermentrout, B., Wechselberger, M. (2009). Canards, Clusters, and Synchronization in a Weakley Coupled Interneuron Model. SIAM Journal on Applied Dynamical Systems, 8(1), 253-278. [More Information]
Wechselberger, M., Weckesser, W. (2009). Homoclinic clusters and chaos associated with a folded node in a stellate cell model. Discrete and Continuous Dynamical Systems - Series S, 2(4), 829-850. [More Information]
Rostein, H., Wechselberger, M., Kopell, N. (2008). Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II Stellate cell model. SIAM Journal on Applied Dynamical Systems, 7(4), 1582-1611. [More Information]
Beck, M., Jones, C., Schaeffer, D., Wechselberger, M. (2008). Electrical Waves in a One-Dimensional Model of Cardiac Tissue. SIAM Journal on Applied Dynamical Systems, 7(4), 1558-1581. [More Information]
Rubin, J., Wechselberger, M. (2008). The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales. Chaos, 18(1), 015105-1-015105-12. [More Information]
Wechselberger, M. (2007). Canards. Scholarpedia, 2(4), 1356-1-1356-7.
Rubin, J., Wechselberger, M. (2007). Giant Squid - Hidden Canard: the 3D Geometry of the Hodgkin Huxley Model. Biological Cybernetics, 97(1), 5-32. [More Information]
Guckenheimer, J., Wechselberger, M., Young, L. (2006). Chaotic attractors of relaxation oscillators. Nonlinearity, 19(3), 701-720. [More Information]
Wechselberger, M., Wright, C., Bishop, G., Boulant, J. (2006). Ionic channels and conductance-based models for hypothalamic neuronal thermosensitivity. American Journal of Physiology - Regulatory Integrative and Comparative Physiology, 291(3), R518-R529. [More Information]
Brons, M., Krupa, M., Wechselberger, M. (2006). Mixed mode oscillations due to the generalized canard phenomenon. Fields Institute Communications, 49, 39-63.
Wechselberger, M. (2005). Existence and bifurcation of canards in R^3 in the case of a folded node. SIAM Journal on Applied Dynamical Systems, 4(1), 101-139. [More Information]
Best, J., Borisyuk, A., Rubin, J., Terman, D., Wechselberger, M. (2005). The dynamic range of bursting in a model respiratory pacemaker network. SIAM Journal on Applied Dynamical Systems, 4(4), 1107-1139. [More Information]
Szmolyan, P., Wechselberger, M. (2004). Relaxation oscillations in R^3. Journal of Differential Equations, 200(1), 69-104. [More Information]
Wechselberger, M. (2002). Extending Melnikov theory to invariant manifolds on non-compact domains. Dynamical Systems-An International Journal, 17(3), 215-233.
Szmolyan, P., Wechselberger, M. (2001). Canards in R^3. Journal of Differential Equations, 177(2), 419-453.

show 56 more

Conferences

Bradshaw-Hajek, B., Lizarraga, I., Marangell, R., Wechselberger, M. (2022). A geometric singular perturbation analysis of regularised reaction-nonlinear diffusion models including shocks. The 47th Sapporo Symposium on Partial Differential Equations, Sapporo: Hokkaido University.
Wechselberger, M. (2005). PoincarÃ© maps for relaxation oscillations in R^3 - invariant manifolds, canards and turning points. EQUADIFF 2003, Hackensack, NJ: World Scientific Publishing.

By Year

Expand all

2025

Miller, T., Tam, A., Marangell, R., Wechselberger, M., Bradshaw- Hajek, B. (2025). Shock selection in reaction–diffusion equations with partially negative diffusivity using nonlinear regularisation. Physica D: Nonlinear Phenomena, 474, 134561-1-134561-14. [More Information]

2024

Bradshaw-Hajek, B., Lizarraga, I., Marangell, R., Wechselberger, M. (2024). A Geometric Singular Perturbation Analysis of Shock Selection Rules in Composite Regularized Reaction-Nonlinear Diffusion Models. SIAM Journal on Applied Dynamical Systems, 23(3), 2099-2137. [More Information]
Miller, T., Tam, A., Marangell, R., Wechselberger, M., Bradshaw-Hajek, B. (2024). Analytic shock-fronted solutions to a reaction–diffusion equation with negative diffusivity. Studies in Applied Mathematics, 153(Open Access), e12685-1-e12685-23. [More Information]
Abelson, D., Di Michiel, J., Frater, C., Pearson, M., Russo, R., Wechselberger, M., Cottee, A., Morgan, L. (2024). Mucus clears from the trachea in a helix: a new twist to understanding airway diseases. Thorax, 79(7), 607-614. [More Information]

2022

Bradshaw-Hajek, B., Lizarraga, I., Marangell, R., Wechselberger, M. (2022). A geometric singular perturbation analysis of regularised reaction-nonlinear diffusion models including shocks. The 47th Sapporo Symposium on Partial Differential Equations, Sapporo: Hokkaido University.
Hester, E., Vasil, G., Wechselberger, M. (2022). On the stability of shocks in isothermal black hole accretion discs. Monthly Notices of the Royal Astronomical Society, 512(4), 5771-5781. [More Information]
Jelbart, S., Pages, N., Kirk, V., Sneyd, J., Wechselberger, M. (2022). Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics. SIAM Journal on Applied Dynamical Systems, 21 (Open Access)(2), 982-1029. [More Information]
Jelbart, S., Kristiansen, K., Szmolyan, P., Wechselberger, M. (2022). Singularly Perturbed Oscillators with Exponential Nonlinearities. Journal of Dynamics and Differential Equations, 34(3), 1823-1875. [More Information]

show 1 more

2021

Lizarraga, I., Rink, B., Wechselberger, M. (2021). Multiple timescales and the parametrisation method in geometric singular perturbation theory. Nonlinearity, 34, 4163-4201. [More Information]
Li, Y., van Heter, P., Simpson, M., Wechselberger, M. (2021). Shock-fronted travelling waves in a reaction–diffusion model with nonlinear forward–backward–forward diffusion. Physica D: Nonlinear Phenomena, 423(Open Access), 132916 - 1-132916 - 14. [More Information]
Jelbart, S., Kristiansen, K., Wechselberger, M. (2021). Singularly perturbed boundary-equilibrium bifurcations. Nonlinearity, 34(11), 7371-7414. [More Information]
Jelbart, S., Kristiansen, K., Wechselberger, M. (2021). Singularly perturbed boundary-focus bifurcations. Journal of Differential Equations, 296, 412-492. [More Information]

show 1 more

2020

Harley, K., van Heijster, P., Marangell, R., Pettet, G., Roberts, T., Wechselberger, M. (2020). (In)stability of travelling waves in a model of haptotaxis. SIAM Journal on Applied Mathematics, 80(4), 1629-1653. [More Information]
Lizarraga, I., Wechselberger, M. (2020). Computational Singular Perturbation Method for Nonstandard Slow-Fast Systems. SIAM Journal on Applied Dynamical Systems, 19(2), 994-1028. [More Information]
Wechselberger, M. (2020). Geometric Singular Perturbation Theory Beyond the Standard Form. Cham: Springer. [More Information]
Avitabile, D., Desroches, M., Veltz, R., Wechselberger, M. (2020). Local Theory for Spatio-Temporal Canards and Delayed Bifurcations. SIAM Journal On Mathematical Analysis, 52(6), 5703-5747. [More Information]
Lizarraga, I., Marangell, R., Wechselberger, M. (2020). Slow Unfoldings of Contact Singularities in Singularly Perturbed Systems Beyond the Standard Form. Journal of Nonlinear Science, 30, 3161-3198. [More Information]
Jelbart, S., Wechselberger, M. (2020). Two-stroke relaxation oscillators. Nonlinearity, 33(5), 2364-2408. [More Information]

show 3 more

2017

Mitry, J., Wechselberger, M. (2017). Folded Saddles and Faux Canards. SIAM Journal on Applied Dynamical Systems, 16(1), 546-596. [More Information]
Carter, P., Knobloch, E., Wechselberger, M. (2017). Transonic canards and stellar wind. Nonlinearity, 30(3), 1006-1033. [More Information]

2016

Boie, S., Kirk, V., Sneyd, J., Wechselberger, M. (2016). Effects of quasi-steady state reduction on biophysical models with oscillations. Journal of Theoretical Biology, 393, 16-31. [More Information]
Hayes, M., Kaper, T., Szmolyan, P., Wechselberger, M. (2016). Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations. Indagationes Mathematicae, 27(5), 1184-1203. [More Information]

2015

Roberts, K., Rubin, J., Wechselberger, M. (2015). Averaging, foIded singularities and torus canards: explaining transitions between bursting and spiking in a coupled neuron model. SIAM Journal on Applied Dynamical Systems, 14(4), 1808-1844. [More Information]
Vo, T., Wechselberger, M. (2015). Canards of folded saddle-node type I. SIAM Journal On Mathematical Analysis, 47(4), 3235-3283. [More Information]
Bertram, R., Tabak, J., Teka, W., Vo, T., Wechselberger, M. (2015). Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells. In R. Bertram, J. Tabak, W. Teka, T. Vo, M. Wechselberger, V. Kirk, J. Sneyd (Eds.), Mathematical Analysis of Complex Cellular Activity, (pp. 1-52). Cham: Springer. [More Information]
Roberts, A., Widiasih, E., Wechselberger, M., Jones, C. (2015). Mixed mode oscillations in a conceptual climate model. Physica D: Nonlinear Phenomena, 292-293, 70-83. [More Information]
De Maesschalck, P., Wechselberger, M. (2015). Neural Excitability and Singular Bifurcations. Journal of Mathematical Neuroscience, 5(16), 1-32. [More Information]
Harley, K., van Heijster, P., Marangell, R., Pettet, G., Wechselberger, M. (2015). Numerical computation of an Evans function for travelling waves. Mathematical Biosciences, 266, 36-51. [More Information]
Ullah, G., Wei, Y., Dahlem, M., Wechselberger, M., Schiff, S. (2015). The Role of Cell Volume in the Dynamics of Seizure, Spreading Depression, and Anoxic Depolarization. PLoS Computational Biology, 11(8), 1-25. [More Information]

show 4 more

2014

Vo, T., Tabak, J., Bertram, R., Wechselberger, M. (2014). A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells. Journal of Computational Neuroscience, 36(2), 259-278. [More Information]
Harley, K., van Heijster, P., Marangell, R., Pettet, G., Wechselberger, M. (2014). Existence of Traveling Wave Solutions for a Model of Tumor Invasion. SIAM Journal on Applied Dynamical Systems, 13(1), 366-396. [More Information]
Harley, K., van Heijster, P., Marangell, R., Pettet, G., Wechselberger, M. (2014). Novel solutions for a model of wound healing angiogenesis. Nonlinearity, 27(12), 2975-3003. [More Information]
Lin, X., Wechselberger, M. (2014). Transonic evaporation waves in a spherically symmetric nozzle. SIAM Journal On Mathematical Analysis, 46(2), 1472-1504. [More Information]

show 1 more

2013

Wechselberger, M., Mitry, J., Rinzel, J. (2013). Canard Theory and Excitability. In Peter E Kloeden, Christian Potzsche (Eds.), Nonautonomous Dynamical Systems in the Life Sciences, (pp. 89-132). Cham, Switzerland: Springer. [More Information]
Vo, T., Tabak, J., Bertram, R., Wechselberger, M. (2013). Canard- and Hopf-induced bursting in pituitary cells. Gazette of the Australian Mathematical Society, 40(3), 199-201.
Mitry, J., McCarthy, M., Kopell, N., Wechselberger, M. (2013). Excitable Neurons, Firing Threshold Manifolds and Canards. Journal of Mathematical Neuroscience, 3(12), 1-32. [More Information]
Vo, T., Bertram, R., Wechselberger, M. (2013). Multiple geometric viewpoints of mixed mode dynamics associated with pseudo-plateau bursting. SIAM Journal on Applied Dynamical Systems, 12(2), 789-830. [More Information]

show 1 more

2012

Wechselberger, M. (2012). A Propos de Canards. Transactions of the American Mathematical Society, 364(6), 3289-3309. [More Information]
Vo, T., Bertram, R., Wechselberger, M. (2012). Bifurcations of canard-induced mixed mode oscillations in a pituitary Lactotroph model. Discrete and Continuous Dynamical Systems - Series A, 32(8), 2879-2912. [More Information]
Desroches, M., Guckenheimer, J., Krauskopf, B., Kuehn, C., Osinga, H., Wechselberger, M. (2012). Mixed-Mode Oscillations with Multiple Time Scales. SIAM Review, 54(2), 211-288. [More Information]

2011

Zhang, W., Kirk, V., Sneyd, J., Wechselberger, M. (2011). Changes in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescales. Journal of Mathematical Neuroscience, 1(9), 1-22. [More Information]
Harvey, E., Kirk, V., Wechselberger, M., Sneyd, J. (2011). Multiple Timescales, Mixed Mode Oscillations and Canards in Models of Intracellular Calcium Dynamics. Journal of Nonlinear Science, 21, 639-683. [More Information]
Teka, W., Tabak, J., Vo, T., Wechselberger, M., Bertram, R. (2011). The dynamics underlying pseudo-plateau bursting in a pituitary cell model. Journal of Mathematical Neuroscience, 1(12), 1-23. [More Information]

2010

Wechselberger, M., Pettet, G. (2010). Folds, canards and shocks in advection-reaction-diffusion models. Nonlinearity, 23, 1949-1969. [More Information]
Krupa, M., Wechselberger, M. (2010). Local analysis near a folded saddle-node singularity. Journal of Differential Equations, 248(12), 2841-2888. [More Information]
Vo, T., Bertram, R., Tabak, J., Wechselberger, M. (2010). Mixed mode oscillations as a mechanism for pseudo-plateau bursting. Journal of Computational Neuroscience, 28(3), 443-458. [More Information]
Harvey, E., Kirk, V., Osinga, H., Sneyd, J., Wechselberger, M. (2010). Understanding anomalous delays in a model of intracellular calcium dynamics. Chaos, 20(4), 045104-1-045104-19. [More Information]

show 1 more

2009

Wechselberger, M., Weckesser, W. (2009). Bifurcations of mixed-mode oscillations in a stellate cell model. Physica D: Nonlinear Phenomena, 238(16), 1598-1614. [More Information]
Ermentrout, B., Wechselberger, M. (2009). Canards, Clusters, and Synchronization in a Weakley Coupled Interneuron Model. SIAM Journal on Applied Dynamical Systems, 8(1), 253-278. [More Information]
Wechselberger, M., Weckesser, W. (2009). Homoclinic clusters and chaos associated with a folded node in a stellate cell model. Discrete and Continuous Dynamical Systems - Series S, 2(4), 829-850. [More Information]

2008

Rostein, H., Wechselberger, M., Kopell, N. (2008). Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II Stellate cell model. SIAM Journal on Applied Dynamical Systems, 7(4), 1582-1611. [More Information]
Beck, M., Jones, C., Schaeffer, D., Wechselberger, M. (2008). Electrical Waves in a One-Dimensional Model of Cardiac Tissue. SIAM Journal on Applied Dynamical Systems, 7(4), 1558-1581. [More Information]
Rubin, J., Wechselberger, M. (2008). The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales. Chaos, 18(1), 015105-1-015105-12. [More Information]

2007

Wechselberger, M. (2007). Canards. Scholarpedia, 2(4), 1356-1-1356-7.
Rubin, J., Wechselberger, M. (2007). Giant Squid - Hidden Canard: the 3D Geometry of the Hodgkin Huxley Model. Biological Cybernetics, 97(1), 5-32. [More Information]

2006

Guckenheimer, J., Wechselberger, M., Young, L. (2006). Chaotic attractors of relaxation oscillators. Nonlinearity, 19(3), 701-720. [More Information]
Wechselberger, M., Wright, C., Bishop, G., Boulant, J. (2006). Ionic channels and conductance-based models for hypothalamic neuronal thermosensitivity. American Journal of Physiology - Regulatory Integrative and Comparative Physiology, 291(3), R518-R529. [More Information]
Brons, M., Krupa, M., Wechselberger, M. (2006). Mixed mode oscillations due to the generalized canard phenomenon. Fields Institute Communications, 49, 39-63.

2005

Wechselberger, M. (2005). Existence and bifurcation of canards in R^3 in the case of a folded node. SIAM Journal on Applied Dynamical Systems, 4(1), 101-139. [More Information]
Wechselberger, M. (2005). PoincarÃ© maps for relaxation oscillations in R^3 - invariant manifolds, canards and turning points. EQUADIFF 2003, Hackensack, NJ: World Scientific Publishing.
Best, J., Borisyuk, A., Rubin, J., Terman, D., Wechselberger, M. (2005). The dynamic range of bursting in a model respiratory pacemaker network. SIAM Journal on Applied Dynamical Systems, 4(4), 1107-1139. [More Information]

2004

Szmolyan, P., Wechselberger, M. (2004). Relaxation oscillations in R^3. Journal of Differential Equations, 200(1), 69-104. [More Information]

2002

Wechselberger, M. (2002). Extending Melnikov theory to invariant manifolds on non-compact domains. Dynamical Systems-An International Journal, 17(3), 215-233.

2001

Szmolyan, P., Wechselberger, M. (2001). Canards in R^3. Journal of Differential Equations, 177(2), 419-453.

Selected Grants

2022

A coordinate-independent theory for multi-time-scale dynamical systems, Wechselberger M, Australian Research Council (ARC)/Discovery Projects (DP)

2020

A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models, Wechselberger M, Marangell R, Hajek B, van Heijster P, Australian Research Council (ARC)/Discovery Projects (DP)

2017

A geometric theory for nonstandard relaxation oscillators, Wechselberger M, Australian Research Council (ARC)/Discovery Projects (DP)

2012

Mathematics of non-communicable diseases: understanding failure of cell signalling, Bogacz R, Kirk V, Krauskopf B, Osinga H, Randall A, Sherman A, Sneyd J, Tsaneva-Atanasova K, Wechselberger M, Office of Global Engagement/IPDF Grant
Geometric methods in mathematicalphysiology, Wechselberger M, Australian Research Council (ARC)/Future Fellowships (FT)

2010

A geometric theory for travelling waves in advection-reaction-diffusion models, Wechselberger M, Pettet G, Jones C, Australian Research Council (ARC)/Discovery Projects (DP)
Diagnostic tools for mixed mode oscillations, Wechselberger M, Guckenheimer J, DVC Research/International Visiting Research Fellowship (IVRF)

2007

Canards and Rifurcations of Spatid-Temporal Patterns, Knobloch E, Wechselberger M, Knobloch E, DVC Research/International Visiting Research Fellowship (IVRF)

2006

Multiple Time Scales Analysis of Physiological Rhythms, Wechselberger M, University of Sydney/Bridging Support

Faculty of Science

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Professor Martin Wechselberger

Timetable

Selected publications

Publications

By Type

By Year

Selected Grants

2022

2020

2017

2012

2010

2007

2006