Brain wave dynamics in a Hopfield-Kuramoto model

Whole brain neural oscillation activities exhibit multiple wave phase patterns and seem to be supported by the common circuit network structure. We proposed a Hopfield Kuramoto model based entirely on heterogeneous connectivity strength rather than phase delay. Multiple wave phase patterns can be encoded in heterogeneous connectivity networks via Hebbian rule and retrieved as attractors. We systematically investigated how the model dynamic landscape influenced by attractors and their corresponding eigenvalues, as well as how to control the stability of equilibrium points and the occurrence of high dimensional bifurcations. This framework enables us to reproduce the dominant wave activity components in human brain functional MRI signal, and provides a canonical model for the multi-body physical system spatio-temporal pattern attractor dynamics.