Discrete network dynamic system for modeling the spread of panic in groups of people

Kalachin S.V., Kalachina E.S.
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The paper addresses the problem of modeling the formation and propagation of panic states in social groups with relatively stable structures of interpersonal interactions. Panic is interpreted as a nonlinear process of emotional contagion arising from the interaction between individual psychological characteristics and collective effects within a social environment. In contrast to models focused on the spatial dynamics of moving crowds, the proposed approach concentrates on quasi-stationary interaction networks that reflect informational and emotional contacts among individuals.

The developed discrete network dynamical system integrates individual temperament parameters (sanguine, choleric, phlegmatic, melancholic), the structure of social connections, and nonlinear mechanisms of collective behavior. The individual dynamics of panic are described using an S-shaped growth function, which ensures boundedness of the emotional arousal level and captures the stages of its formation and saturation. Social influence is modeled on a graph of interpersonal interactions (an Erdos –Renyi random network) through local contacts between individuals.

Additionally, the model incorporates the effects of collective contagion and avalanche-like amplification driven by the average panic level in the group, as well as a baseline stress factor depending on group size. Numerical simulation is implemented in a discrete iterative form, allowing for the analysis of both individual and group panic trajectories. A quantitative indicator of the panic propagation rate is introduced, defined by the time required for the group to reach a state close to full panic.

A comparative analysis of heterogeneous and homogeneous groups is conducted, demonstrating that group heterogeneity significantly accelerates panic propagation due to inter-temperament interactions: highly excitable individuals act as initiators of emotional contagion, while more stable individuals partially dampen its dynamics. The evaluation of the model quality using the coefficient of determination shows a high degree of consistency within the simulation data.

The practical significance of the work lies in the potential application of the model for analyzing the resilience of social groups to panic states, assessing risks at mass events, and developing intelligent systems for monitoring collective behavior. Future research directions include extending the model to account for directed and dynamic networks, as well as its calibration based on empirical data.

Keywords: panic state, emotional contagion, network modeling, nonlinear dynamics, social interactions, numerical simulation
Citation in English: Kalachin S.V., Kalachina E.S. Discrete network dynamic system for modeling the spread of panic in groups of people // Computer Research and Modeling, 2026, vol. 18, no. 2, pp. 483-499
Citation in English: Kalachin S.V., Kalachina E.S. Discrete network dynamic system for modeling the spread of panic in groups of people // Computer Research and Modeling, 2026, vol. 18, no. 2, pp. 483-499
DOI: 10.20537/2076-7633-2026-18-2-483-499
URL: http://crm-en.ics.org.ru/journal/article/3719/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2026 Kalachin S.V., Kalachina E.S.

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