Pattern classification and its relation with topology of dynamical systems manifolds

A novel method of neural network for classification is presented. The neural network consists of order parameters each of those corresponds to an unique stored prototype. These parameters connected to each other by the matrix of weights which can be predetermined accordingly to the required partition of the whole set of prototypes into classes or subsets. The subsets may intersects if any prototype belongs to several classes. The classification performs via the temporal competition between subsets of order parameters. This leads to the representation of attractive manifolds in the phase space, when each manifold corresponds to a subset.