Emotional Dynamics in Social Interactions: A Multi-Strategy Synergy Model

This paper presents a mathematical model for analyzing emotional dynamics in social interactions, considering strategic induction, group feedback, and natural emotional decay. Stability analysis shows that without control strategies, an emotional system has a unique stable equilibrium. Numerical simulations validated the model’s effectiveness. Single-strategy analyses revealed that social comparison and emotional resonance strategies can significantly enhance emotional levels, while a self-positioning strategy causes emotional oscillations. Composite-strategy simulations showed that combined strategies led to an initial rapid increase in emotions, followed by periodic fluctuations and stabilization. Global sensitivity analysis identified the natural emotional decay rate as the most influential parameter for emotional dynamics. An empirical case study of commuters’ weekly emotional changes demonstrated the model’s ability to capture real-world emotional fluctuations. Overall, the model provides a fundamental mathematical framework for understanding emotional regulation in social contexts, laying the groundwork for further exploration of related psychological and sociological issues.