Evaluation of ELF Electric Fields Effects on Bifurcation Phenomenon of Spaced-Clamped Coductance-Based Minimal Cell Models

Abstract

Spaced clamped Conductance-Based minimal cell models, main basis of more complex neuronal models, e.g. Hodgkin-Huxley model. In this paper, these models have been modified under the influence of ELF electric fields and induced depolarization as a result of such fields is added to the their Nernst potential. By using bifurcation analysis of dynamical systems and considering the injected current and induced voltage as generic parameters of models, the occurrence of dynamical behaviors is justified. Results of this research shows that due to the existence of only an amplifying gating variable and one resonant gating variable in structure of models, bistability phenomenon is caused by Hopf, limit point and LPC (Limit Point Cycle) bifurcations occur and multi-stabilities of higher order than two do not occur. Our simulation results show that the minimal models, INa,p+Ih and Ih+IKir, have maximum and minimum dynamical variations, respectively.