Multi-parameter Hopf-bifurcation in HHM Model Exposed to ELF Electric Field

The variation of cell trans-membrane voltage exposed to extremely low frequency (ELF) electric field is analyzed; a modified Hodgkin-Huxley model of muscle (HHM) is established by introducing a new parameter denoting the effect of external electric field, and the bifurcation caused by the new parameter as well as leakage conductance and sodium ions anti-electromotive force is studied. The algebra criterion in high dimension equations is employed to perform the analysis of multi-parameter dynamical bifurcation. The results are of biological significance and suggest that the aberration of dynamics in bio-systems may be accounted for diseases caused by electric exposure.