This study characterizes the neurophysiological mechanisms underlying electromagnetic imaging signals using stability analysis. Researchers have proposed that transitions between conscious awake and anaesthetised states, and other brain states more generally, may result from system stability changes. The concept of stability in dynamical systems theory provides a mathematical framework to describe this possibility. In particular, the degree to which a system's trajectory in phase space is affected by small perturbations determines the stability. Previous studies using linear or oscillator-based whole-brain models cannot represent complex cerebrocortical dynamics, or model parameters were pre-assumed or inferred from data but did not change over time. This study proposes a nonlinear neurophysiologically plausible whole-cortex modeling framework to analyze the stability of brain dynamics for the emergence and disappearance of consciousness using time-varying parameters estimated from the data.Clinical relevance- Depth of anaesthesia is typically measured through changes in EEG statistics like the bispectral index and spectral entropy. However, these monitors have been found to fail in preventing awareness during surgery and postoperative recall. Our whole-cortex stability analysis may be useful in measuring anaesthesia levels in clinical settings, as it changes with the level of consciousness and is independent of individual differences and anaesthetic agents. The proposed method can also be used to, for example, identify critical brain regions for consciousness, locate the epileptogenic zone and investigate the dominance of extrinsic or intrinsic factors in brain functions.