Neuronal population dynamic model:An analytic approach |
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Authors: | Wentao Huang Licheng Jiao Yuelei Xu Shiping Ma Jianhua Jia |
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Institution: | 1. Institute of Intelligent Information Processing,Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education,Xidian University,P.O.Box 224,Xi'an 710071,China 2. Department of Avionics Engineering,Engineering College of Air Force Engineering University,Xi'an 710038,China |
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Abstract: | A novel analytic approach is presented to study the population of excitatory and inhibitory spiking neurons in this paper. The evolution in time of the population dynamic equation is determined by a partial differential equation. A new function is proposed to characterize the population of excitatory and inhibitory spiking neurons, which is different from the population density function discussed by most researchers. And a novel evolution equation, which is a nonhomogeneous parabolic type equation, is derived. From this, the stationary solution and the firing rate of the stationary states are given. Last, by the Fourier transform, the time dependent solution is also obtained. This method can be used to analyze the various dynamic behaviors of neuronal populations. |
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Keywords: | Analytic approach Neuronal population Dynamic model Fourier transform |
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