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In the paper, based on the theory of neurodynamics, the nine-dimensional one-compartment complex model of CA1 pyramid neuron developed by David Golomb [ J. Neurophysiol .,  96  (2006), 1912–1926] is reduced, and the two-dimensional reduced neuron model is obtained for the first time. According to the definition of the minimal model, the nine-dimensional complex dynamic model has first be reduced to the minimal models. Then the minimal model is reduced into the two-dimensional model by the model reduction theory of neurodynamics and the polynomial regression algorithm. Finally, dynamic characteristics of the two-dimensional reduced neuron model are analyzed and discussed in detail by the neurodynamic analysis methods. When the stimulation current gradually increases from zero, the two-dimensional reduced neuron model undergoes the saddle-node bifurcation. It is equivalent to a bistable integrator and has the common dynamic properties of the integrator such as definite threshold value and class 2 neural excitability. The investigation provides a simple and convenient method to investigate deeply the high-dimensional complex neuron model’s dynamic characteristics and functions by the neurodynamic theory. Moreover, it is helpful to know the dynamic characteristics of the hippocampal neuron.

Study on the Complex Neuron Model’s Reduction and Its Dynamic Characteristics