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neuronal population dynamic model: An analytic approach

Progress in Natural Science:Materials International 2009年第9期19卷 1159-1163页

作者： Wentao Huang a, Licheng Jiao a, Yuelei Xub, Shiping Ma b, Jianhua Jia a a 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 b Department of Avionics Engineering, Engineering College of Air Force Engineering University, Xi’an 710038, China 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 Department of Avionics Engineering Engineering College of Air Force Engineering University Xi’an 710038 China

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.

关键词： Analytic approach neuronal population Dynamic model Fourier transform

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Phase-response synchronization in neuronal population

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Science China(Technological Sciences) 2014年第5期57卷 923-928页

作者： JIAO XianFa ZHU DanFeng School of Mathematics Hefei University of Technology

In this study,we have formulated the phase description of the neuronal oscillator with non-instantaneous synaptic inputs and external periodic stimulus by using the phase sensitivity *** numerical simulation,we have found that the phase of a neuronal oscillator undergoes periodic evolution or locked state,which is determined by the synaptic time *** synaptic time constant is also an important condition under which the global network is *** the synaptic time constant is relatively small,perfectly synchronized behavior quickly occurs in the neuronal *** the synaptic time constant becomes slightly larger,periodic synchronization emerges in the neuronal ***,synchronized activity in the neuronal population is lost for larger synaptic time *** external periodic stimulus can change the synchronization patterns in the neuronal *** a weak low-frequency stimulus,the neuronal populations quick synchronized bursting;whereas a high-frequency stimulus can produce synchronized overlapping *** have also found that neuronal oscillators with type-II phase response curves are more susceptible to synchronization than those with type-I phase response curves.

关键词： neuronal population phase response curve synaptic input external periodic stimulus

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