Generalized and partial synchronization of coupled neural networks

Synchronization of neural signals has been proposed as a temporal coding sc heme representing cooperated computation in distributed cortical networks. Previous theoretical studies in that direction mainly focused on the synchr onization of coupled oscillatory subsystems and neglected more complex dyna mical modes, that already exist on the single-unit level. In this paper we study the parametrized rime-discrete dynamics of two coupled recurrent netw orks of graded neurons. Conditions for the existence of partially synchroni zed dynamics of these systems are derived, referring to a situation where o nly subsets of neurons in each sub-network are synchronous. The coupled net works can have different architectures and even a different number of neuro ns. Periodic as well as quasiperiodic and chaotic attractors constrained to a manifold M of synchronized components are observed. Examples are discuss ed for coupled 3-neuron networks having different architectures, and for co upled 2-neuron and 3-neuron networks. Partial synchronization of different degrees is demonstrated by numerical results for selected sets of parameter s. In conclusion, the results show that synchronization phenomena far beyon d completely synchronized oscillations can occur even in simple coupled net works. The type of the synchronization depends in an intricate way on stimu li, history and connectivity as well as other parameters of the network. Sp ecific inputs can further switch between different operational modes in a c omplex way, suggesting a similarly rich spatio-temporal behaviour in real n eural systems.