Analysis Of Bifurcation And Chaos In Hodgkin-Huxley Model

The research on the electromagnetic effect to the human being has been paid muchattention recently. On the one hand, the diseases caused by electromagnetic field arereported more and more frequently. On the other hand, the clinical researches haveshown that some diseases can be cured by special selected electromagnetic fields. Thenerve system plays a very important role in the modulation and control of thephysiologic enginery. The external stimulus are taken by the neurons of the nervesystem, and coded, propagated and decoded by means of various patterns of nervefiber discharge. Different patterns of discharge reflect the difference of the externalstimulus information and induce diverse physiological effect. A comprehensive studyon the quantitive relationship between the patterns of nerve fiber discharge and theexternal electromagnetic fields is of important, theoretical and practical significancein defending human being against the diseases caused by electromagnetic fields moreeffectively and in making good use of the electromagnetic effect in clinical medicine.The electrophysiological function of nerve system contains very complex nonlineardynamical behaviors. In this paper, the dynamical characteristics of Hodgkin-Huxley(HH) model exposed to low frequency electric fields are studied by employing thenonlinear dynamical theory and methods such as bifurcation and chaos.With the aid of algebra criterion for Hopf bifurcation in high dimension equations,the Hopf bifurcation points with the intensity of DC current or/and DC electrical fieldas the bifurcation parameters are calculated numerically. The parameter region intwo-dimensional space in which the stable periodic solutions exist is obtained. Thestimulation results also showed the DC stimulus parameter range of different patternsof the discharge. By employing the theory of chaos, the patterns of nerve fiberdischarge are examined under periodic electric stimulus with various frequencies. Thecomplex nonlinear dynamics such as periodic, quasi-periodic and chaotic behaviors ofdischarge patterns are found. The frequency ranges of diverse discharge patterns aregiven, which can provide some instructions to the establishment of the standard ofenvironmental conservation and to the application of electric stimulus in clinicalmedicine.