Search Results - "Wechselberger, Martin"

The Role of Cell Volume in the Dynamics of Seizure, Spreading Depression, and Anoxic Depolarization by Ullah, Ghanim, Wei, Yina, Dahlem, Markus A, Wechselberger, Martin, Schiff, Steven J

“…Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little of how cell volume affects neuronal dynamics…”
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Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model by Rubin, Jonathan, Wechselberger, Martin

“…This work is motivated by the observation of remarkably slow firing in the uncoupled Hodgkin-Huxley model, depending on parameters tau( h ), tau( n ) that…”
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{A} propos de canards (Apropos canards) by WECHSELBERGER, MARTIN

“…We extend canard theory of singularly perturbed systems to the general case of k fast dimensions, with k\ge 2 arbitrary. A folded critical manifold of a…”
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Bifurcations of mixed-mode oscillations in a stellate cell model by Wechselberger, Martin, Weckesser, Warren

“…Experimental recordings of the membrane potential of stellate cells within the entorhinal cortex show a transition from subthreshold oscillations (STOs) via…”
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Multiple Timescales, Mixed Mode Oscillations and Canards in Models of Intracellular Calcium Dynamics by Harvey, Emily, Kirk, Vivien, Wechselberger, Martin, Sneyd, James

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Ionic channels and conductance-based models for hypothalamic neuronal thermosensitivity by Wechselberger, Martin, Wright, Chadwick L, Bishop, Georgia A, Boulant, Jack A

“…Thermoregulatory responses are partially controlled by the preoptic area and anterior hypothalamus (PO/AH), which contains a mixed population of…”
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Local analysis near a folded saddle-node singularity by Krupa, Martin, Wechselberger, Martin

“…Folded saddle-nodes occur generically in one parameter families of singularly perturbed systems with two slow variables. We show that these folded…”
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Singularly perturbed boundary-focus bifurcations by Jelbart, Samuel, Kristiansen, Kristian Uldall, Wechselberger, Martin

“…We consider smooth systems limiting as ϵ→0 to piecewise-smooth (PWS) systems with a boundary-focus (BF) bifurcation. After deriving a suitable local normal…”
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Shock-fronted travelling waves in a reaction–diffusion model with nonlinear forward–backward–forward diffusion by Li, Yifei, van Heijster, Peter, Simpson, Matthew J., Wechselberger, Martin

“…Reaction–diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates…”
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Mixed-Mode Oscillations with Multiple Time Scales by Desroches, Mathieu, Guckenheimer, John, Krauskopf, Bernd, Kuehn, Christian, Osinga, Hinke M., Wechselberger, Martin

“…Mixed-mode oscillations (MMOs) are trajectories of a dynamical system in which there is an alternation between oscillations of distinct large and small…”
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Slow Unfoldings of Contact Singularities in Singularly Perturbed Systems Beyond the Standard Form by Lizarraga, Ian, Marangell, Robert, Wechselberger, Martin

“…We develop the contact singularity theory for singularly perturbed (or ‘slow–fast’) vector fields of the general form z ′ = H ( z , ε ) , z ∈ R n and 0 < ε ≪ 1…”
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The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales by Rubin, Jonathan, Wechselberger, Martin

“…In recent work [J. Rubin and M. Wechselberger, Biol. Cybern. 97, 5 (2007)], we explained the appearance of remarkably slow oscillations in the classical…”
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Mucus clears from the trachea in a helix: a new twist to understanding airway diseases by Abelson, David, Di Michiel, James, Frater, Clayton, Pearson, Mark, Russo, Robert, Wechselberger, Martin, Cottee, Alice, Morgan, Lucy

“…Mucociliary clearance (MCC) is critical to lung health and is impaired in many diseases. The path of MCC may have an important impact on clearance but has…”
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On the stability of shocks in isothermal black hole accretion discs by Hester, Eric W, Vasil, Geoffrey M, Wechselberger, Martin

“…ABSTRACT Most black holes possess accretion discs. Models of such discs inform observations and constrain the properties of the black holes and their…”
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Effects of quasi-steady-state reduction on biophysical models with oscillations by Boie, Sebastian, Kirk, Vivien, Sneyd, James, Wechselberger, Martin

“…Many biophysical models have the property that some variables in the model evolve much faster than others. A common step in the analysis of such systems is to…”
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Mixed mode oscillations as a mechanism for pseudo-plateau bursting by Vo, Theodore, Bertram, Richard, Tabak, Joel, Wechselberger, Martin

“…We combine bifurcation analysis with the theory of canard-induced mixed mode oscillations to investigate the dynamics of a novel form of bursting. This…”
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Multiple Timescales, Mixed Mode Oscillations and Canards in Models of Intracellular Calcium Dynamics by Harvey, Emily, Kirk, Vivien, Wechselberger, Martin, Sneyd, James

“…A range of representative models of intracellular calcium dynamics are surveyed, with the aim of determining which model characteristics are qualitatively…”
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Mixed mode oscillations in a conceptual climate model by Roberts, Andrew, Widiasih, Esther, Wechselberger, Martin, Jones, Christopher K.R.T.

“…Much work has been done on relaxation oscillations and other simple oscillators in conceptual climate models. However, the oscillatory patterns in climate data…”
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Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations by Hayes, Michael G., Kaper, Tasso J., Szmolyan, Peter, Wechselberger, Martin

“…In this article, we present a new, geometric proof of known results for slow passage through Hopf bifurcations (Baer et al. (1989), Neishtadt (1987, 1988),…”
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A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells by Vo, Theodore, Tabak, Joël, Bertram, Richard, Wechselberger, Martin

“…The electrical activity of endocrine pituitary cells is mediated by a plethora of ionic currents and establishing the role of a single channel type is…”
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