Here the almost sure convergence of one-dimensional Kohonen's
algorithm in its general form, namely, the 2k-neighbor setting with a
nonuniform stimuli distribution, is proved. We show that the asymptotic
behavior of the algorithm is governed by a cooperative system of differential
equations which is irreducible. The system of differential equations possesses
an asymptotically stable equilibrium, a compact subset of whose domain of
attraction will be visited by the state variable $X^n$ infinitely often. The
assumptions on the stimuli distribution and the neighborhood functions are
weakened, too.