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Martin Wechselberger

Martin Wechselberger

D-Index & Metrics

Mathematics

D-Index
30
Citations
4056
World Ranking
3508
National Ranking
81

Overview

Martin Wechselberger is affiliated with the University of Sydney in Australia. Their research spans multiple fields including Physics and Astronomy, Mathematics, and Computer Science, with significant contributions across these disciplines.

Wechselberger's main areas of study include:

  • Nonlinear Dynamics and Pattern Formation
  • Stochastic Dynamics and Bifurcation
  • Advanced Differential Equations and Dynamical Systems
  • Mathematical and Theoretical Epidemiology and Ecology Models
  • Differential Equations and Numerical Methods
  • Quantum Chaos and Dynamical Systems
  • Advanced Thermodynamics and Statistical Mechanics

They have published extensively on subfields such as Statistical and Nonlinear Physics, Computer Networks and Communications, Geometry and Topology, Numerical Analysis, and Public Health, Environmental and Occupational Health.

Recent papers authored or co-authored by Wechselberger include:

  • "Two-stroke relaxation oscillators," 2020, Nonlinearity
  • "Local Theory for Spatio-Temporal Canards and Delayed Bifurcations," 2020, SIAM Journal on Mathematical Analysis
  • "Shock-fronted travelling waves in a reaction-diffusion model with nonlinear forward-backward-forward diffusion," 2021, Physica D Nonlinear Phenomena
  • "(In)stability of Travelling Waves in a Model of Haptotaxis," 2020, SIAM Journal on Applied Mathematics
  • "Singularly Perturbed Oscillators with Exponential Nonlinearities," 2021, Journal of Dynamics and Differential Equations

Their frequent co-authors include Robert Marangell, Ian Lizarraga, Samuel Jelbart, Bronwyn H. Bradshaw-Hajek, and Bob Rink.

Wechselberger has contributed to several publication venues, with notable frequent appearances in:

  • arXiv (Cornell University)
  • Nonlinearity
  • SIAM Journal on Applied Dynamical Systems
  • Physica D Nonlinear Phenomena
  • SIAM Journal on Mathematical Analysis

They have published a book titled Geometric Singular Perturbation Theory Beyond the Standard Form (2020) under Springer International Publishing.

Best Publications

  • Mixed-Mode Oscillations with Multiple Time Scales

    Mathieu Desroches;John Guckenheimer;Bernd Krauskopf;Christian Kuehn

  • Canards in R3

    Peter Szmolyan;Martin Wechselberger

  • Existence and Bifurcation of Canards in R^3 in the Case of a Folded Node

    Martin Wechselberger

  • Mixed Mode Oscillations due to the Generalized Canard Phenomenon

    Morten Brøns;Martin Krupa;Martin Wechselberger

  • Local analysis near a folded saddle-node singularity

    Martin Krupa;Martin Wechselberger

  • Giant squid-hidden canard: the 3D geometry of the Hodgkin–Huxley model

    Jonathan Rubin;Martin Wechselberger

  • Relaxation oscillations in R3

    P. Szmolyan;M. Wechselberger

  • À propos de canards (Apropos canards)

    Martin Wechselberger

  • Geometric Singular Perturbation Theory Beyond the Standard Form

    Martin Wechselberger

  • The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales.

    Jonathan Rubin;Martin Wechselberger

  • Canard Induced Mixed-Mode Oscillations in a Medial Entorhinal Cortex Layer II Stellate Cell Model ∗

    Horacio G. Rotstein;Martin Wechselberger;Nancy Kopell

  • Chaotic attractors of relaxation oscillators

    John Guckenheimer;Martin Wechselberger;Lai Sang Young

  • The Role of Cell Volume in the Dynamics of Seizure, Spreading Depression, and Anoxic Depolarization.

    Ghanim Ullah;Yina Wei;Markus A Dahlem;Martin Wechselberger

  • Multiple Timescales, Mixed Mode Oscillations and Canards in Models of Intracellular Calcium Dynamics

    Emily P. Harvey;Vivien Kirk;Martin Wechselberger;James Sneyd

  • The Dynamic Range of Bursting in a Model Respiratory Pacemaker Network

    Janet Best;Alla Borisyuk;Jonathan E. Rubin;David Terman

  • Mixed mode oscillations as a mechanism for pseudo-plateau bursting

    Theodore Vo;Richard Bertram;Joel Tabak;Martin Wechselberger

  • Canards, Clusters, and Synchronization in a Weakly Coupled Interneuron Model

    Bard Ermentrout;Martin Wechselberger

  • Excitable Neurons, Firing Threshold Manifolds and Canards

    John Mitry;Michelle McCarthy;Nancy Kopell;Martin Wechselberger

  • Bifurcations of mixed-mode oscillations in a stellate cell model

    Martin Wechselberger;Warren Weckesser

  • Multiple Geometric Viewpoints of Mixed Mode Dynamics Associated with Pseudo-plateau Bursting

    Theodore Vo;Richard Bertram;Martin Wechselberger

Frequent Co-Authors

Richard Bertram
Richard Bertram Florida State University
Jonathan E. Rubin
Jonathan E. Rubin University of Pittsburgh
Hinke M. Osinga
Hinke M. Osinga University of Auckland
Nancy Kopell
Nancy Kopell Boston University
Christopher K. R. T. Jones
Christopher K. R. T. Jones University of North Carolina at Chapel Hill
John Guckenheimer
John Guckenheimer Cornell University
Matthew J. Simpson
Matthew J. Simpson Queensland University of Technology
John Rinzel
John Rinzel New York University
Steven J. Schiff
Steven J. Schiff Yale University
Georgia A. Bishop
Georgia A. Bishop The Ohio State University

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