Cellular neural field and its convergence analysis

A new continuum model complementary to traditional cellular neural networks is introduced in this note. We consider a cellular neural field formed by infinitely many cellular neurons and modelled by an integrodifferential equation. Then, using LaSalle's invariance principle on Banach space, we show that the field quantity will asymptotically converge to an equilibrium state under the condition that all equilibria of the system are isolated. From the practical sense, the convergence indicates the essential capability of retrieving message from original raw data.