极低频电场下HHM模型的多参数Hopf分岔分析.pdf

ofUle24mChinese Proceedlngs ControlConference GuanMhou,P．R．Chlna July工5-l2005 极低频电场下HHM模型的多参数Hopf分岔分析 车艳秋，王 江，李立 (天津大学电气与自动化工程学院，天津大学，300072) E-mail：jiangwang@1|ju．edu．cn 摘要：基于跨膜电压的时空特性分析了极低频电场下细胞跨膜电压的变化规律；建立了引入外电场参数的改进 的肌肉中Hodgken-Huxlcy(珈孤D模型。采用高维方程的代数判据方法，研究了该改进模型下以漏电导、钠离子 反电动势及电场扰动为参数的多参数Hopf分岔，分析方法简便。研究结果解释了相应的生理过程，并试图从 生物系统动态过程异变的角度探讨外加极低频电场下生理疾病的成因。 关键词：多参数，Hopf分，Hodgken-Huxley模型，外电场 Multi—parameter in Model Hopf-bifurcation Hodgkin-Huxley toELF ExposedExternalElectricField Chc YahqiU，WangJiang．“Li andAutomation (SchoolofElectrical Eng．，77anjinUniversi印．Tianfin300072) Abstract：Basedonresultsof characteristicsoftrans．membrane space-time variationofcell voltage．the trans-membrane to low voltageexposed fieldis modified extremelyfrequency(ELF)electricanalyzed．A isestablished anew of Hodgkin-Huxley(HH)model theeffectextemalelectric byintroducingparameterdenoting thebifurcationcausedthenew aswelIas field，and by conductanceandsodiumions parameter leakage anti-electromotiveforcciSstudied．Thecriterionin dimension iS to the algebra high equationsemployedperform of bifurcation．Theresultsareof analysismulti·parameter and thatthe dy