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

作者：Peng Yueping^*

来源：International Journal of Nonlinear Sciences and Numerical Simulation, 2015, 16(3-4): 129-139.

DOI：10.1515/ijnsns-2013-0093

• neurodynamics
• the reduced neuron model
• bifurcation
• computer simulation

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.

• 出版日期2015-6
• 单位西安交通大学; 中国人民武装警察部队工程大学