Memorize multiple phase pattern attractors in nonlinear coupled oscillators dynamic via heterogeneous connectivity strength

Abstract

Whole brain neural oscillation activities exhibit multiple wave patterns and seem to be supported by the common circuit network structure. We proposed a Hebbian-like Kuramoto model based entirely on heterogeneous connectivity strength rather than phase delay, which encodes the multiple phase patterns 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 dimension 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.