Mutual synchronization and clustering in randomly coupled chaotic dynamical networks

We introduce and study systems of randomly coupled maps where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally coupled maps) until a certain critical threshold for the connectivity is reached. We further show that not only the average connectivity, but also the architecture of the couplings is responsible for the cluster structure observed. We analyze the different phases of the system and use various correlation measures in order to detect ordered nonsynchronized states. Finally, it is shown that the system displays a,dynamical hierarchical clustering which allows the definition of emerging graphs. [S1063-651X(99)04908-9].