Cycle-symmetric matrices and convergent neural networks

This work investigates a class of neural networks with cycle-symmetric connection strength. We shall show that, by changing the coordinates, the convergence of dynamics by Fiedler and Gedeon [Physica D 111 (1998) 288] is equivalent to the classical results. This presentation also addresses the extension of the convergence theorem to other classes of signal functions with saturations. In particular, the result of Cohen and Grossberg [IEEE Trans. Syst. Man Cybernet. SMC-13 (1983) 815] is recast and extended with a more concise verification.