Complete Synchronization in Coupled Neuromodules of Different Types

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-integrateand-fire 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 different 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-fire 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. ∗appeared in: Theory in Biosciences, 118, 267–283 (1999).