Modeling and analyzing phantom crowd stampedes through emotion accumulation, behavioral synchronization, and collision propagation

High-density evacuations often escalate rapidly, with seemingly minor local pushing amplifying into crowd shockwaves and even phantom crowd stampedes. However, this important phenomenon is challenging to analyze for improving crowd management, because existing models underrepresent how emotional accumulation, lateral push synchronization, and chain collision propagation jointly drive such emergent dynamics. To bridge this gap, we first incorporate sustained bodily contact into the emotion model and establish a sequential sampling model to describe how emotional accumulation dynamically triggers behavioral transitions. Second, we introduce a lateral synchronization mechanism to represent how local pushing rhythms spontaneously align and evolve from disordered, multi-rhythmic interactions into regular crowd shockwaves. Third, after accounting for pedestrians' passive postural adjustment when losing balance, an inverted pendulum model is applied to reproduce chain collision propagation. Simulation results demonstrate improved prediction of high-risk zones compared with previous models. To suppress pushing emotions, we further introduce a spatially decaying management term. On this basis, we evaluate spatial deployment principles and identify “high-risk priority + dispersed within the area” as a more effective layout. Lastly, we derive an empirical formula for the maximum safe evacuee count as a function of exit width, number of security units, and initial proportion of pushers, to support both pre-planning and real-time assessment of management effectiveness. Overall, the proposed model provides a nonlinear-dynamics–based interpretation of how microscopic emotional fluctuations self-organize into macroscopic shockwaves, offering mechanistic insight and quantitative tools for anticipating and mitigating critical crowd instabilities. • We model how crowd pushing turns into shockwaves and raises stampede risk. • Sustained contact is shown to drive emotion growth and behavioral imitation. • High-risk areas lie near the exit sides rather than the center in front. • Empirical formula estimates safe evacuees from exit width, staffing, and pushers. • Dispersed placement within high-risk areas lowers pushing and injuries.