Title：The Hindmarsh-Rose neuron model Bifurcation analysis and piecewise-linear approximations

Abstract：This paper provides a global picture of the bifurcation scenario of the Hindmarsh–Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh–Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters. © 2008 American Institute of Physics. 【DOI: 10.1063/1.2975967】

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标题：Hindmarsh-Rose 神经元模型：分岔分析和分段近似

摘要：本文给出了 Hindmarsh-Rose 模型分岔情形的全局图。将数值模拟与数值延拓相结合，用于展开复杂分岔结构。通过改变两个分岔参数进行分岔分析，有迹象表明所发现的结构具有普遍性，适用于各种分岔参数组合。然后，然后利用有关组织原理和分岔图的信息，将模型的动力学与为电路实现而特别设计的分段线性逼近模型的动力学进行比较。结果表明，模型的动力学现象具有良好的匹配性。这些结果可用于设计Hindmarsh-Rose 模型模拟神经响应的多样性的电路实现，并作为预测模型动力学现象的指南，以及作为参数函数的电路实现。© 2008 American Institute of Physics.[ DOI：10.1063/1.2975967]

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