Analytical Solution for Dynamic of Neuronal Populations
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.
KeywordsFiring Rate Neuronal Population Neural Computation Computational Neuroscience Time Dependent Solution
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