Stability of a neutral delay neuron system in the critical case

In this paper, the asymptotic stability properties of neutral-type neuron system are studied mainly in the critical case when the exponential stability is not possible. In the case of a critical value of the coefficient in neutral-type neuron system, the difficulty for our investigation is the fact that the spectrum of the linear operator is asymptotically approximated to the imaginary axis. Hence, based on the energy method, the asymptotic stability results for neutral-type neuron system are derived, and a complete analysis of the stability diagram is presented.