Bursting Analysis

  1. Multi-Timescale Systems and Fast-Slow Analysis
    Richard Bertram and Jonathan E. Rubin
    Mathematical Biosciences , 287:105-121, (2017).

  2. 2016
  3. From Global to Local: Exploring the Relationship Between Parameters and Behaviors in Models of Electrical Excitability
    Patrick Fletcher, Richard Bertram, Joel Tabak
    Journal of Computational Neuroscience, 40:331-345, (2016).

  4. 2015
  5. Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells
    Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger
    In Mathematical Analysis of Complex Cellular Activity, Frontiers in Applied Dynamical Systems: Reviews and Tutorials, Springer, 1:1-52, (2015).

  6. 2014
  7. A Geometric Understanding of How Fast Activating Potassium Channels Promote Bursting in Pituitary Cells
    Theodore Vo, Joel Tabak, Richard Bertram, Martin Wechselberger
    Journal of Computational Neuroscience, 36:259-278, (2014).

  8. 2013
  9. Multiple Geometric Viewpoints of Mixed Mode Dynamics Associated with Pseudo-Plateau Bursting
    Theodore Vo, Richard Bertram, Martin Wechselberger
    SIAM Journal of Applied Dynamical Systems, 12:789-830, (2013).
    Winner of 2017 SIAM Outstanding Paper Prize

  10. 2012
  11. The Relationship Between Two Fast/Slow Analysis Techniques for Bursting Oscillations
    Wondimu Teka, Joel Tabak, Richard Bertram
    Chaos, 22:043117, (2012).

  12. Bifurcations of Canard-Induced Mixed Mode Oscillations in a Pituitary Lactotroph Model
    Theodore Vo, Richard Bertram, Martin Wechselberger
    Discrete and Continuous Dynamical Systems, 32:2879-2912, (2012).

  13. 2011
  14. The Dynamics Underlying Pseudo-Plateau Bursting in a Pituitary Cell Model
    Wondimu Teka, Joel Tabak, Theodore Vo, Martin Wechselberger, Richard Bertram
    Journal of Mathematical Neuroscience, 1(12): doi:10.1186/2190-8567-1-12, (2011).

  15. From Plateau to Pseudo-Plateau Bursting: Making the Transition
    Wondimu Teka, Krasimira Tsaneva-Atanasova, Richard Bertram, Joel Tabak
    Bulletin of Mathematical Biology, 73:1292-1311, (2011).

  16. Slow Variable Dominance and Phase Resetting in Phantom Bursting
    Margaret Watts, Joel Tabak, Charles Zimliki, Arthur Sherman, Richard Bertram
    Journal of Theoretical Biology, 276:218-228, (2011).

  17. 2010
  18. Mixed Mode Oscillations as a Mechanisms for Pseudo-Plateau Bursting
    Theodore Vo, Richard Bertram, Joel Tabak, Martin Wechselberger
    Journal of Computational Neuroscience, 28:443-458, (2010).

  19. 2008
  20. A-Type K+ Current Can Act as a Trigger for Bursting in the Absence of a Slow Variable
    Natalia Toporikova, Joel Tabak, Marc E. Freeman, Richard Bertram
    Neural Computation, 20:436-451, (2008).

  21. 2005
  22. Negative Calcium Feedback: The Road from Chay-Keizer
    Richard Bertram and Arthur Sherman
    In Bursting: The Genesis of Rhythm in the Nervous System
    edited by S. Coombes and P. Bressloff, World Scientific Press, pp. 19-48, (2005).

  23. 1995
  24. Topological and Phenomenological Classification of Bursting Oscillations
    Richard Bertram, Manish J. Butte, Tim Kiemel, Arthur Shermam
    Bulletin of Mathematical Biology, 57:413-439, (1995).

  25. 1994
  26. Reduced-System Analysis of the Effects of Serotonin on a Molluscan Burster Neuron
    Richard Bertram
    Biological Cybernetics, 70:359-368, (1994).