Oscillator Network Spectra, Chimeras, and Transient Dynamics in the Non-Asymptotic Limit
Abstract
A fundamental problem in network science is to establish connections between the structure of a network and the resulting non-linear dynamics on the network. Here, we employ a recently introduced complex-valued approach to the finite Kuramoto Model, which is a canonical model used throughout neuroscience to study neural synchronization. This analytical approach connects network structure to emergent dynamics through the eigensystem of a composed matrix incorporating the network adjacency matrix, coupling strength and phase lag. We apply this approach in the non-asymptotic limit to generate (1) a mechanistic theory of finite chimera dynamics and (2) a method for predicting relaxation time to synchrony. These findings highlight a rare example where we can link network structure to the emergent non-linear dynamics analytically, bolstering the utility of novel approaches in network theory that include operator-based methods and extensions to higher order number fields.