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Numerical Results on the Hodgkin-Huxley Neural Network: Spikes Annihilation

  • Dragos Calitoiu
  • John B. Oommen
  • Doron Nussbaum
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4729)

Abstract

One of various families of Neural Networks (NN) that have been used in the study and development of the field of Artificial Intelligence (AI) is the Hodgkin-Huxley (HH) Network. In addition to the computational properties of the HH neuron, it also can be used to reasonably model biological phenomena, and in particular, in modeling neurons which are “synchronized/desynchronized”. The HH Neuron is a nonlinear system with two equilibrium states: A fixed point and a limit cycle. Both of them co-exist and are stable. By using a perturbation method, the behavior of this neuron can be switched between these two equilibria, namely spiking and resting respectively. The process of changing from spiking to resting is referred to as Spike Annihilation. In this paper, we numerically prove the existence of a brief excitation (input) which, when delivered to the HH neuron during its repetitively firing state, annihilates its spikes. We also derive the characteristics of this brief excitation.

Keywords

Hopf Bifurcation Bifurcation Point Stable Limit Cycle Pulse Stimulus Unstable Limit Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Calitoiu, D.: Chaotic Systems for Pattern Recognition and Brain Modelling. Ph.D. Thesis, Carleton University (2006)Google Scholar
  2. 2.
    Wilson, H.: Spikes decisions and actions: Dynamical foundations of neuroscience. Oxford University Press, Oxford (1999)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Dragos Calitoiu
    • 1
  • John B. Oommen
    • 2
  • Doron Nussbaum
    • 1
  1. 1.Carleton University, Ottawa, K1S 5B6Canada
  2. 2.IEEE and IAPR, Carleton University, Ottawa, K1S 5B6Canada

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