The human brain, with its intricate web of billions of neurons and trillions of synaptic connections, is a remarkable organ responsible for performing complex cognitive processes. While brain imaging techniques like fMRI and EEG provide insights into neural activity, there is no broadly accepted mathematical framework for the collaborative activity of neuronal populations and their communication. In the interdisciplinary fields of neuroscience and computational modelling, this research introduces a data-driven mathematical framework for modelling the brain's cortical network, derived from EEG data, while incorporating an exogenous input. This framework captures brain dynamics, forming a state-space model using subspace identification, and evaluates statistical dependencies among brain sources, known as functional connectivity. Employed on a dataset mimicking a sensorimotor task, it proves effective in characterizing brain dynamics, with the PO-MOESP method outperforming N4SID. Additionally, the framework is competent to assess functional connectivity between brain sources, resulting in a network connectivity diagram that offers valuable insights into the statistical relationships between distinct brain regions. Altogether, it is concluded the designed algorithm can determine the intricate interactions within the brain during a simple passively performed task stimulating the brain. Consequently, this achievement forms a robust foundation for advancing Brain-Computer Interfaces (BCIs) and enhancing the diagnosis of neurological disorders.