Suicidal thoughts and behaviors have a large impact both on the individual affected by them and their surroundings. Despite efforts to predict active attempts, prediction has not improved over the last 50 years. The most reliable finding is that suicidal ideation (SI) is an important driver for suicide attempts. Recent studies often find nonlinear patterns in the progression of SI. Incorporating these phenomena into the conceptualization of SI could help us improve prediction and understand important antecedents to an attempt. While collecting ecological momentary assessment (EMA) data is both time-, and cost-intensive, computational modeling is an accessible way to model SI based on theory and analyze data for target phenomena. This study investigated data patterns simulated from the formalized General Escape Theory of Suicide for nonlinear behavior to validate the model and to understand when nonlinear patterns occur. The simulation modeled 1008 individuals over four weeks. Critical cases were identified through multiple analyses including changepoint analysis, calculating the bimodality coefficient, and hidden Markov models. Overall, the results show that 4 in 1008 individuals have the expected nonlinear patterns. These results can inform efforts to validate and adjust the formal model. Furthermore, interpreting parameter values and assessing which variables are most likely to induce nonlinear patterns could help identify critical cases within clinical settings.