Driving neuromodulesinto synchronous chaos

Abstract

We discuss the time-discrete parametrized dynamics of two neuromodules, which axe coupled in a uni-directional way. General conditions for the existence of synchronized dynamics are derived for these systems. It is demonstrated that already the one-way couplings of 2- neuron modules can result in periodic, quasiperiodic as well as chaotic dynamics constrained to a synchronization manifold M. Stability of the synchronized dynamics is calculated by conditional Lyapunov exponents. In addition to synchronized attractors there often co-exist asynchronous periodic, quasiperiodic or even chaotic attractors. Simulation results for selected sets of parameters are presented.