谢勇

Date:

2025-04-30

Title of Paper:

Dynamic behavior analysis of fractional-order Hindmarsh–Rose neuronal model

Journal:

Cognitive Neurodynamics

Summary:

Previous experimental work has shown that the firing rate of multiple time-scales of adaptation for single
rat neocortical pyramidal neurons is consistent with fractional-order differentiation, and the fractional-order neuronal models depict the firing rate of neurons more verifiably than other models do. For this reason, the dynamic characteristics of the fractional-order Hindmarsh–Rose (HR) neuronal model were here investigated. The results showed several obvious differences in dynamic characteristic between the fractional-order HR neuronal model and an integer-ordered model. First, the fractionalorder HR neuronal model displayed different firing modes (chaotic firing and periodic firing) as the fractional order changed when other parameters remained the same as in the integer-order model. However, only one firing mode is displayed in integer-order models with the same parameters.
The fractional order is the key to determining the firing mode. Second, the Hopf bifurcation point of this fractional-order model, from the resting state to periodic firing, was found to be larger than that of the integer-order
model. Third, for the state of periodically firing of fractional- order and integer-order HR neuron model, the firing
frequency of the fractional-order neuronal model was greater than that of the integer-order model, and when the
fractional order of the model decreased, the firing frequency increased。

Co-author:

Dong Jun, Zhang Guang-jun, Xie Yong, Yao Hong, Wang Jue

Volume:

8(2)

Page Number:

167-175,

Translation or Not:

No

Date of Publication:

2014-12-01