New stability conditions for Hopfield networks in partial simultaneous update mode.
Cernuschi-Frías has proposed a partial simultaneous updating (PSU) mode for Hopfield networks. He also derived sufficient conditions to ensure global stability. In this letter, a counter-example is given to illustrate that the PSU sequence may converge to limited cycles even if one uses a connection matrix satisfying the Cernuschi-Frías conditions. Then, new sufficient conditions ensuring global convergence of a Hopfield network in PSU mode are derived. Compared with the result of fully parallel mode case, the new result permits a little relaxation on the lower bound of the main diagonal elements of the connection matrix.
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