Browsing by Author Wechselberger, Martin

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Issue DateTitleAuthor(s)Citation
2015Averaging, foIded singularities and torus canards: explaining transitions between bursting and spiking in a coupled neuron modelRoberts, Kerry-Lyn; Wechselberger, Martin; Rubin, Jonathan; Mathematics & Statistics; Mathematics & StatisticsAveraging, foIded singularities and torus canards: explaining transitions between bursting and spiking in a coupled neuron model, SIAM Journal on Applied Dynamical Systems, vol.14, 4, 2015,pp 1808-1844
2012Bifurcations of canard-induced mixed mode oscillations in a pituitary Lactotroph modelVo, Theodore; Wechselberger, Martin; Bertram, Richard; Mathematics & Statistics; Mathematics & StatisticsBifurcations of canard-induced mixed mode oscillations in a pituitary Lactotroph model, Discrete and Continuous Dynamical Systems - Series A, vol.32, 8, 2012,pp 2879-2912
2009Bifurcations of mixed-mode oscillations in a stellate cell modelWechselberger, Martin; Weckesser, Warren; Mathematics & Statistics; Mathematics & StatisticsBifurcations of mixed-mode oscillations in a stellate cell model, Physica D: Nonlinear Phenomena, vol.238, N/A,pp 1598-1614
2008Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II Stellate cell modelWechselberger, Martin; Kopell, Nancy; Rostein, Horacio G; Mathematics & StatisticsCanard induced mixed-mode oscillations in a medial entorhinal cortex layer II Stellate cell model, SIAM Journal on Applied Dynamical Systems, vol.7, 4, 2008,pp 1582-1611
2013Canard Theory and ExcitabilityMitry, John; Wechselberger, Martin; Rinzel, J; Mathematics & Statistics; Mathematics & StatisticsCanard Theory and Excitability in Nonautonomous Dynamical Systems in the Life Sciences, Springer, 2013, pp. 89-132
2015Canards of folded saddle-node type IVo, Theodore; Wechselberger, Martin; Mathematics & Statistics; Mathematics & StatisticsCanards of folded saddle-node type I, SIAM Journal On Mathematical Analysis, vol.47, 4, 2015,pp 3235-3283
2009Canards, Clusters, and Synchronization in a Weakley Coupled Interneuron ModelWechselberger, Martin; Ermentrout, Bard; Mathematics & StatisticsCanards, Clusters, and Synchronization in a Weakley Coupled Interneuron Model, SIAM Journal on Applied Dynamical Systems, vol.8, 1, 2009,pp 253-278
2011Changes in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescalesWechselberger, Martin; Kirk, Vivien; Sneyd, James; Zhang, Wenjun; Mathematics & StatisticsChanges in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescales, Journal of Mathematical Neuroscience, vol.1, 9, 2011,pp 1-22
2006Chaotic attractors of relaxation oscillatorsWechselberger, Martin; Guckenheimer, John; Young, Lai-Sang; Mathematics & StatisticsChaotic attractors of relaxation oscillators, Nonlinearity, vol.19,(3),2006,pp 701-720
2011The dynamics underlying pseudo-plateau bursting in a pituitary cell modelVo, Theodore; Wechselberger, Martin; Bertram, Richard; Tabak, Joel; Teka, Wondimu; Mathematics & Statistics; Mathematics & StatisticsThe dynamics underlying pseudo-plateau bursting in a pituitary cell model, Journal of Mathematical Neuroscience, vol.1, N/A, 2011,pp No. 12-(23pp)
2016Effects of quasi-steady state reduction on biophysical models with oscillationsWechselberger, Martin; Boie, Sebastian; Kirk, Vivien; Sneyd, James; Mathematics & StatisticsEffects of quasi-steady state reduction on biophysical models with oscillations, Journal of Theoretical Biology, vol.393, N/A, 2016,pp 16-31
2008Electrical Waves in a One-Dimensional Model of Cardiac TissueWechselberger, Martin; Beck, Margaret; Jones, Christopher K.R.T.; Schaeffer, David; Mathematics & StatisticsElectrical Waves in a One-Dimensional Model of Cardiac Tissue, SIAM Journal on Applied Dynamical Systems, vol.7, 4, 2008,pp 1558-1581
2014Existence of Traveling Wave Solutions for a Model of Tumor InvasionMarangell, Robert; Wechselberger, Martin; Harley, K; Pettet, Graeme; van Heijster, Petrus; Mathematics & Statistics; Mathematics & StatisticsExistence of Traveling Wave Solutions for a Model of Tumor Invasion, SIAM Journal on Applied Dynamical Systems, vol.13, 1, 2014,pp 366-396
2017Folded Saddles and Faux CanardsMitry, John; Wechselberger, Martin; Mathematics & Statistics; Mathematics & StatisticsFolded Saddles and Faux Canards, SIAM Journal on Applied Dynamical Systems, vol.16, 1, 2017,pp 546-596
2010Folds, canards and shocks in advection-reaction-diffusion modelsWechselberger, Martin; Pettet, Graeme; Mathematics & StatisticsFolds, canards and shocks in advection-reaction-diffusion models, Nonlinearity, vol.23, N/A, 2010,pp 1949-1969
2016Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcationsWechselberger, Martin; Hayes, Michael; Kaper, Tasso; Szmolyan, Peter; Mathematics & StatisticsGeometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations, Indagationes Mathematicae, vol.27, 5, 2016,pp 1184-1203
2015Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary CellsVo, Theodore; Wechselberger, Martin; Bertram, Richard; Tabak, Joel; Teka, W; Mathematics & Statistics; Mathematics & StatisticsGeometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells in Mathematical Analysis of Complex Cellular Activity, Springer, 2015, pp. 1-52
2014A geometric understanding of how fast activating potassium channels promote bursting in pituitary cellsVo, Theodore; Wechselberger, Martin; Bertram, Richard; Tabak, Joel; Mathematics & Statistics; Mathematics & StatisticsA geometric understanding of how fast activating potassium channels promote bursting in pituitary cells, Journal of computational neuroscience, vol.36, 2, 2014,pp 259-278
2009Homoclinic clusters and chaos associated with a folded node in a stellate cell modelWechselberger, Martin; Weckesser, Warren; Mathematics & Statistics; Mathematics & StatisticsHomoclinic clusters and chaos associated with a folded node in a stellate cell model, Discrete and Continuous Dynamical Systems - Series S, vol.2, 4,pp 829-850
2006Ionic channels and conductance-based models for hypothalamic neuronal thermosensitivityWechselberger, Martin; Bishop, Georgia A; Boulant, Jack A; Wright, Chadwick L; Mathematics & StatisticsIonic channels and conductance-based models for hypothalamic neuronal thermosensitivity, American Journal of Physiology: Regulatory, Integrative and Comparative Physiology, vol.291,(3),2006,pp R518-R529