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Computational and Mathematical Methods in Medicine
Volume 2014, Article ID 761907, 9 pages
http://dx.doi.org/10.1155/2014/761907
Research Article

Effects of Maximal Sodium and Potassium Conductance on the Stability of Hodgkin-Huxley Model

1Biocomputing Research Center, School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001, China
2School of Physics & Astronomy, University of Manchester, Manchester, UK

Received 13 February 2014; Revised 12 June 2014; Accepted 15 June 2014; Published 3 July 2014

Academic Editor: Rui Jiang

Copyright © 2014 Yue Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Hodgkin-Huxley (HH) equation is the first cell computing model in the world and pioneered the use of model to study electrophysiological problems. The model consists of four differential equations which are based on the experimental data of ion channels. Maximal conductance is an important characteristic of different channels. In this study, mathematical method is used to investigate the importance of maximal sodium conductance and maximal potassium conductance . Applying stability theory, and taking and as variables, we analyze the stability and bifurcations of the model. Bifurcations are found when the variables change, and bifurcation points and boundary are also calculated. There is only one bifurcation point when is the variable, while there are two points when is variable. The ( ,   ) plane is partitioned into two regions and the upper bifurcation boundary is similar to a line when both and are variables. Numerical simulations illustrate the validity of the analysis. The results obtained could be helpful in studying relevant diseases caused by maximal conductance anomaly.