Synchronization detection using spatial ordinal partitions in networks

We use a robust methodology that enables us to detect synchronous regions in networks of coupled dynamical systems and identify their collective behaviors. Our method employs ordinal patterns of spatial configuration of neighbor oscillators at each time point to ascertain whether or not neighboring nodes in a network are synchronized. We then use permutation entropy and forbidden sequence cardinality to classify collective behavior. We first demonstrate the effectiveness of our method on a time series of coupled identical logistic maps that are located on a ring. Our method not only confirms previous findings of collective behavior identification but also shows the borders of synchronous regions when oscillators of a network are partially synchronized. Then we apply our findings to a network of logistic maps with random connections to demonstrate the method's efficacy in situations where the network's spatiotemporal plots are not feasible.