Journal of Computational Neuroscience

, Volume 36, Issue 1, pp 81–95 | Cite as

Low dimensional model of bursting neurons

  • X. Zhao
  • J. W. Kim
  • P. A. Robinson
  • C. J. Rennie


A computationally efficient, biophysically-based model of neuronal behavior is presented; it incorporates ion channel dynamics in its two fast ion channels while preserving simplicity by representing only one slow ion current. The model equations are shown to provide a wide array of physiological dynamics in terms of spiking patterns, bursting, subthreshold oscillations, and chaotic firing. Despite its simplicity, the model is capable of simulating an extensive range of spiking patterns. Several common neuronal behaviors observed in vivo are demonstrated by varying model parameters. These behaviors are classified into dynamical classes using phase diagrams whose boundaries in parameter space prove to be accurately delineated by linear stability analysis. This simple model is suitable for use in large scale simulations involving neural field theory or neuronal networks.


Bursting neuron Linear stability analysis Ion channel models 



This work was supported by the Australian Research Council and the Westmead Millennium Institute.

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • X. Zhao
    • 1
    • 2
    • 3
    • 4
  • J. W. Kim
    • 1
    • 2
    • 4
  • P. A. Robinson
    • 1
    • 2
    • 4
  • C. J. Rennie
    • 1
    • 2
    • 4
  1. 1.School of PhysicsThe University of SydneySydneyAustralia
  2. 2.Brain Dynamics Center, Sydney Medical School-WesternUniversity of SydneyWestmeadAustralia
  3. 3.Faculty of MedicineThe University of SydneySydneyAustralia
  4. 4.Center for Integrated Research and Understanding of SleepGlebeAustralia

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