A Dynamic Fitting Method for Hybrid Time-Delayed and Uncertain Internally-Coupled Complex Networks: From Kuramoto Model to Neural Mass Model

The human brain, with its intricate network of neurons and synapses, remains one of the most complex systems to understand and model. The study presents a groundbreaking approach to understanding complex neural networks by introducing a dynamic fitting method for hybrid time-delayed and uncertain internally-coupled complex networks. Specifically, the research focuses on integrating a Neural Mass Model (NMM) called Jansen-Rit Model (JRM) with the Kuramoto model, by utilizing real human brain structural data from Diffusion Tensor Imaging (DTI), as well as functional data from Electroencephalography (EEG) and Magnetic Resonance Imaging (MRI), the study extends above two models into a more comprehensive brain-like model. This innovative multimodal model enables the simultaneous observation of frequency variations, synchronization states, and simulated electrophysiological activities, even in the presence of internal coupling and time delays. A parallel fast heuristics algorithm serves as the global optimization method, facilitating rapid convergence to a stable state that closely approximates real human brain dynamics. The findings offer a robust computational tool for neuroscience research, with the potential to simulate and understand a wide array of neurological conditions and cognitive states. This research not only advances our understanding of complex neural dynamics but also opens up exciting possibilities for future interdisciplinary studies by further refine or expand upon the current model.