In this paper, we investigate the local stability of the diagonal recurrent neural network (DRNN), a particular case of recurrent neural netwroks, in which a recurrent neuron only possesses a self-feedback connection. The local stability conditions for a DRNN are presented. Subsequently it is shown how the extent of stability can be investigated in terms of the equilibrium state's region of attraction in state space. Then, some examples are given to illustrate the stability problem of diagonal recurrent neural networks.
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