Qualitative behaviour of some simple networks

Some classical neural network systems including the Hartline-Ratliff system, the Linsker system, and the general sigmoid dynamics, are reconsidered within a more general class of dynamical systems. For synchronous dynamics the existence, uniqueness, local and global stability of stationary points is investigated. For asynchronous dynamics a convergence theorem is proved. The application of the theory of quasimonotone flows leads to some insights so far not widespread in network theory.