High-order couplings in geometric complex networks of neurons.

We explore the consequences of introducing higher-order interactions in a geometric complex network of Morris-Lecar neurons. We focus on the regime where traveling synchronization waves are observed from a first-neighbors-based coupling to evaluate the changes induced when higher-order dynamical interactions are included. We observe that the traveling-wave phenomenon gets enhanced by these interactions, allowing the activity to travel further in the system without generating pathological full synchronization states. This scheme could be a step toward a simple phenomenological modelization of neuroglial networks.

Dynamical complexity as a proxy for the network degree distribution.

We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the nodes is found to be a function of their topological roles, with nodes of higher degree displaying lower levels of complexity. We provide several examples of theoretical models of chaotic oscillators, pulse-coupled neurons, and experimental networks of nonlinear electronic circuits evidencing such a hierarchical behavior. Importantly, our results imply that it is possible to infer the degree distribution of a network only from individual dynamical measurements.