二维和三维分数阶Hindmarsh-Rose型神经元模型的分析
Analysis of two- and three-dimensional fractional-order Hindmarsh-Rose type neuronal models
摘要：
对二维和三维分数阶Hindmarsh-Rose神经元模型进行了理论分析，重点研究了系统的分数阶数作为分岔参数时，系统的稳定性和Hopf分岔的发生.为了验证理论结果，我们还进行了数值模拟，揭示了三维分数阶慢-快系统中丰富的猝发行为。
英文摘要：
A theoretical analysis of two- and three-dimensional fractional-order Hindmarsh-Rose neuronal models is presented, focusing on stability properties and occurrence of Hopf bifurcations, with respect to the fractional order of the system chosen as bifurcation parameter. With the aim of exemplifying and validating the theoretical results, numerical simulations are also undertaken, which reveal rich bursting behavior in the three-dimensional fractional-order slow-fast system.
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