Abstract

We discuss the parametrized dynamics of two coupled recurrent neural networks comprising either additive sigmoid neurons in discrete time or biologically more plausible time-continuous leaky-integrate-and- re cells. General conditions for the existence of synchronized activity in such networks are given, which guarantee that corresponding neurons in both coupled sub-networks evolve synchronously. It is, in particular, demonstrated that even the coupling of totally di erent network structures can result in complex dynamics constrained to a synchronization manifold M. For additive sigmoid neurons the synchronized dynamics can be periodic, quasiperiodic as well as chaotic, and its stability can be determined by Lyapunov exponent techniques. For leaky-integrate-and- re cells synchronized orbits are typically periodic, often with an extremely long period duration. In addition to synchronized attractors there often co-exist asynchronous periodic, quasiperiodic and even chaotic attractors.

Citations