Analytical solution for dynamic of neuronal populations

Authors:
Wentao Huang;Licheng Jiao;Shiping Ma;Yuelei Xu
Affiliations:
Institute of Intelligent Information Processing and Key Laboratory, of Radar Signal Processing, Xidian University, Xi’an, China;Institute of Intelligent Information Processing and Key Laboratory, of Radar Signal Processing, Xidian University, Xi’an, China;Signal and Information Processing Laboratory, Avionic Engineering Department, College of Engineering, Air Force Engineering University, Xi’an, China;Signal and Information Processing Laboratory, Avionic Engineering Department, College of Engineering, Air Force Engineering University, Xi’an, China
Venue:
ICANN'05 Proceedings of the 15th international conference on Artificial Neural Networks: biological Inspirations - Volume Part I
Year:
2005

Citing 3
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Abstract

The population density approach is a viable method to describe the large populations of neurons and has generated considerable interest recently. The evolution in time of the population density is determined by a partial differential equation. Now, the discussion of most researchers is based on the population density function. In this paper, we propose a new function to characterize the population of excitatory and inhibitory spiking neurons and derive a novel evolution equation which is a nonhomogeneous parabolic type equation. Moreover, we study the stationary solution and give the firing rate of the stationary states. Then we solve for the time dependent solution using the Fourier transform, which can be used to analyze the various behavior of cerebra.