Computing brain networks with complex dynamics

The interplay between neuronal network connectivity and neuron dynamics is known to drive global brain behavior; however, the exact relationship between network connectivity and node dynamics is complex and remains poorly understood. Previous theoretical and modeling work has shown that in small toy networks, when nodes are equipped with discrete quadratic dynamics, properties of the emergent behavior of the complex quadratic network (CQN) can give rise to features that relate to the underlying topology. Specifically, when the long-term behavior of CQNs is represented by asymptotic fractal sets, certain topological features of the fractal can be used to classify the network topology. However, the success of this approach has thus far not been tested on more complex real-world networks. Here, we apply a CQN modeling approach to capture individual differences in real-world brain networks derived from human connectome data. We show that CQNs are more sensitive than traditional graph theoretic measures at capturing individual differences in the topology of the human connectome, and that features of the associated equi-M sets can differentiate between male and female connectomes. This study, therefore, provides a basis upon which future work can build in order to better quantify individual differences in brain connectivity, and how these differences drive brain function and behavior.