Biological Cybernetics

, Volume 107, Issue 1, pp 15–24 | Cite as

Firing patterns in a conductance-based neuron model: bifurcation, phase diagram, and chaos

  • Y. Qi
  • A. L. Watts
  • J. W. Kim
  • P. A. Robinson
Original Paper


Responding to various stimuli, some neurons either remain resting or can fire several distinct patterns of action potentials, such as spiking, bursting, subthreshold oscillations, and chaotic firing. In particular, Wilson’s conductance-based neocortical neuron model, derived from the Hodgkin–Huxley model, is explored to understand underlying mechanisms of the firing patterns. Phase diagrams describing boundaries between the domains of different firing patterns are obtained via extensive numerical computations. The boundaries are further studied by standard instability analyses, which demonstrates that the chaotic neural firing could develop via period-doubling and/or period- adding cascades. Sequences of the firing patterns often observed in many neural experiments are also discussed in the phase diagram framework developed. Our results lay the groundwork for wider use of the model, especially for incorporating it into neural field modeling of the brain.


Action potential Conductance-based neuron model Linear stability analysis Period-doubling/adding route to chaos 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Y. Qi
    • 1
  • A. L. Watts
    • 1
  • J. W. Kim
    • 1
    • 2
  • P. A. Robinson
    • 1
    • 2
    • 3
  1. 1.School of PhysicsThe University of SydneySydneyAustralia
  2. 2.Center for Integrated Research and Understanding of SleepWoolcock Institute of Medical ResearchGlebeAustralia
  3. 3.Brain Dynamics Center, Sydney Medical School—WesternThe University of SydneyWestmeadAustralia

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