Two-parameter bifurcation in a two-dimensional simplified Hodgkin-Huxley model
Two-parameter bifurcation in a two-dimensional simplified Hodgkin-Huxley model
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DOI：
10.1016/j.cnsns.2012.06.022
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Hu Wang;Yongguang Yu;Ran Zhao;Sha Wang
中科院分区：
文献类型：
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作者：
Hu Wang;Yongguang Yu;Ran Zhao;Sha Wang
通过定性分析和数值模拟研究了二维简化Hodgkin-Huxley模型在外电场作用下的动力学行为。给出了系统存在Hopf分支的充分必要条件。研究了平衡点和极限环的稳定性。此外，还讨论了简化模型和原模型中鸭翼和分岔现象。简化模型的动力学行为与原模型一致。这对进一步研究原始模型有很大的帮助。
The dynamical behaviors of a two-dimensional simplified Hodgkin–Huxley model exposed to external electric fields are investigated based on the qualitative analysis and numerical simulation. A necessary and sufficient condition is given for the existence of the Hopf bifurcation. The stability of equilibrium points and limit cycles is also studied. Moreover, the canards and bifurcation are discussed in the simplified model and original model. The dynamical behaviors of the simplified model are consistent with the original model. It would be a great help to further investigations of the original model.