In this study, we present a scenario-based approach to investigate the protest potential in society using mathematical tools from graph theory and simulation modeling. The research aims to construct a cognitive map that reflects key factors, such as population deprivation levels, overall well-being, social fears, trust in authority, social expectations, and stability of social structures. We report the results of a scenario analysis of the developed model, obtaining forecasted scenarios of the dynamics of society's protest potential under various conditions and influences. At the core of this research is the examination of a complex system's possible response to external destructive impacts, and we propose a set of measures to counteract these influences on societal dynamics. The scenario methodology combines graph theory for representing complex relationships between key factors and simulation modeling for predicting potential developmental scenarios. Conducting this study required modifying the traditional mathematical apparatus of cognitive modeling. We developed methods and algorithms for scenario-event identification of the model's significant factors' behavior and utilizing the results of such identification when forming complex functional relationships in the scenario model. In generating scenarios, the range of events is significantly expanded compared to traditional cognitive modeling approaches, which could have been overlooked but may be crucial for situational analysis.