Multi-parameter Hopf-bifurcation in Hodgkin–Huxley model exposed to ELF external electric field

The interference between external electric exposure and biological objects is discussed. Based on results of space–time characteristics of trans-membrane voltage, the variation of cell trans-membrane voltage exposed to extremely low frequency (ELF) electric field is analyzed; a modified Hodgkin–Huxley (HH) model 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 account for diseases caused by electric exposure.