Analysis of stability of neural network with inhibitory neurons |
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Authors: | Yan Liu Rubin Wang Zhikang Zhang Xianfa Jiao |
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Institution: | (1) Institute for Cognitive Neurodynamics, East China University of Science and Technology, 200237 Shanghai, People’s Republic of China;(2) Department of Mathematics, School of Science, Hefei University of Technology, Hefei, People’s Republic of China |
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Abstract: | Phase coding in a neural network composed of neural oscillators with inhibitory neurons was studied based on the theory of
stochastic phase dynamics. We found that with increasing the coupling coefficients of inhibitory neural oscillators, the firing
density in excitatory population transits to a critical state. In this case, when we increase the inhibitory coupling, the
firing density will come into dynamic balance again and tend to a fixed value gradually. According to the phenomenon, in the
paper we found parameter regions to exhibit those different population states, called dividing zones including flat fading
zone, rapid fading zone and critical zone. Based on the dividing zones we can choose the number ratio between inhibitory neurons
and excitatory neurons in the neural network, and estimate the coupling action of inhibitory population and excitatory population.
Our research also shows that the balance value, enabling the firing density to reach the dynamic balance, does not depend
on initial conditions. In addition, the critical value in critical state is only related to the number ratio between inhibitory
neurons and excitatory neurons, but is independent of inhibitory coupling and excitatory coupling. |
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Keywords: | Inhibitory neural population Excitatory neural population Average number density Critical state |
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