We propose a mathematical model for a working memory using Hodgkin-Huxley neurons of one compartment. We assume that there exist excitatory neurons and inhibitory neurons, and each excitatory neuron is distinguished as a selective neuron or a non-selective neuron. Selective neurons are assumed to form subpopulations in which a selective neuron does not belong to more than one subpopulation. Synaptic strengths between neurons within a subpopulation are imposed to be potentiated. By numerical simulations, we show that persistent firing occurs in a subpopulation of selective neurons, which corresponds to the retention of memory as the function of the working memory. Furthermore, we obtain different results depending on the strength of NMDA synapse and the strength of external input; if we enhance the strength of external input to a subpopulation while the persistent firing is occurring in other subpopulations, the persistent firing occurs in the subpopulation or is sustained against the external input. These results show that the effects of neuroinodulation and the strength of external input have an important role in the working memory.
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