Synchronous and Asynchronous Chaos in Coupled Neuromodules

The parametrized time-discrete dynamics of two recurrently coupled neuromodules is studied analytically and by computer simulations. Conditions for the existence of synchronized dynamics are derived and periodic as well as quasiperiodic and chaotic attractors constrained to a synchronization manifold M are observed. Stability properties of the synchronized dynamics is discussed by using Lyapunov exponents parallel and transversal to the synchronization manifold. Simulation results are presented for selected sets of parameters. It is observed that locally stable synchronous dynamics often co-exists with asynchronous periodic, quasiperiodic or even chaotic attractors. ∗published in: International Journal of Bifurcation and Chaos, 9, 1957–1968 (1999).