| 一类细胞膜离子通道模型的分岔及混沌研究 |
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| 引用本文： | 宋自根,李群宏,徐洁琼,魏艳辉.一类细胞膜离子通道模型的分岔及混沌研究[J].河南师范大学学报(自然科学版),2007,35(2):1-4. |
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| 作者姓名： | 宋自根 李群宏 徐洁琼 魏艳辉 |
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| 作者单位： | 广西大学,数学与信息科学学院,南宁,530004 |
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| 基金项目： | 国家自然科学基金
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广西科学基金
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广西研究生教育创新项目 |
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| 摘 要： | 以一类细胞膜离子通道模型为研究对象,定性分析其系统定态的存在性和稳定性,讨论了系统的鞍结分岔和Hopf分岔,并利用Melnikov方法深入研究了该模型可能发生的混沌运动,给出了系统发生混沌运动时参数必须满足的临界条件,从而试图从生物系统动态过程异变的角度探讨生理疾病的成因过程,为疾病治疗提供了机理解释,也为医药研制提供了线索.
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| 关 键 词： | 离子通道 鞍结分岔 Hopf分岔 混沌 Melnikov方法 |
| 文章编号： | 1000-2367(2007)02-0001-04 |
| 修稿时间： | 2006-05-09 |
Study on Bifurcation and Chaos of an Ion Channel Model in Cell Membrane |
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| SONG Zi-gen,LI Qun-hong,XUE jie-qiong,WEI Yan-hui.Study on Bifurcation and Chaos of an Ion Channel Model in Cell Membrane[J].Journal of Henan Normal University(Natural Science),2007,35(2):1-4. |
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| Authors: | SONG Zi-gen LI Qun-hong XUE jie-qiong WEI Yan-hui |
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| Institution: | School of Mathematics and Information Science,Guangxi University, Nanning 530004,China |
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| Abstract: | The nonlinear dynamical model of ion channel in cell membrane is taken for as a study object,and the existence and stability of its steady states are qualitatively analyzed.The Saddle-node bifurcation and Hopf bifurcation are discussed.Furthermore,its potential chaotic motions are further studied by means of Melnikov's method and the parameters for the occurrence of chaotic motions are obtained.So the paper tries to prove that the aberrance occurred in the dynamic biological process may be accounted for such diseases,and offered the mechanism explanation and the clue of the medicament study. |
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| Keywords: | ion channel saddle-node bifurcation Hopf bifurcation chaos Melnikov's method |
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