Neuronal population dynamic model: An analytic approach

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.

[1]  Nicolas Brunel,et al.  Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons , 2000, Journal of Computational Neuroscience.

[2]  Maoguo Gong,et al.  Response Analysis of Neuronal Population with Synaptic Depression , 2005, NIPS.

[3]  Gregory D. Smith,et al.  A two-dimensional population density approach to modeling the dLGN/PGN network , 2006, Neurocomputing.

[4]  Lawrence Sirovich,et al.  A Population Study of Integrate-and-Fire-or-Burst Neurons , 2002, Neural Computation.

[5]  Lawrence Sirovich,et al.  Populations of Tightly Coupled Neurons: The RGC/LGN System , 2008, Neural Computation.

[6]  Alain Destexhe,et al.  Analytical Integrate-and-Fire Neuron Models with Conductance-Based Dynamics for Event-Driven Simulation Strategies , 2006, Neural Computation.

[7]  Stefan Rotter,et al.  Correlations and Population Dynamics in Cortical Networks , 2008, Neural Computation.

[8]  Lawrence Sirovich,et al.  On the Simulation of Large Populations of Neurons , 2004, Journal of Computational Neuroscience.

[9]  Lawrence Sirovich,et al.  Dynamics of neuronal populations: eigenfunction theory; some solvable cases , 2003, Network.

[10]  Cheng Ly,et al.  Critical Analysis of Dimension Reduction by a Moment Closure Method in a Population Density Approach to Neural Network Modeling , 2007, Neural Computation.

[11]  Duane Q. Nykamp,et al.  A Population Density Approach That Facilitates Large-Scale Modeling of Neural Networks: Analysis and an Application to Orientation Tuning , 2004, Journal of Computational Neuroscience.

[12]  Marc de Kamps,et al.  A Simple and Stable Numerical Solution for the Population Density Equation , 2003, Neural Computation.

[13]  Bruce W. Knight,et al.  Dynamics of Encoding in Neuron Populations: Some General Mathematical Features , 2000, Neural Computation.