Journal
COGNITIVE NEURODYNAMICS
Volume 8, Issue 2, Pages 167-175Publisher
SPRINGER
DOI: 10.1007/s11571-013-9273-x
Keywords
Fractional-order; Hopf bifurcation; HR model; Transition of firing mode
Categories
Funding
- National Science Foundation [10872156, 81071150, 10972170]
- Shaanxi Province Science Foundation [2007014, 2012JM8035]
- Chinese Post-doctorate Foundation [20080430203]
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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 fractional-order 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.
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