A dynamical systems model of emotional contagion: Oscillatory coupling in the circumplex of affect

Background Emotional contagion plays a crucial role in shaping group dynamics, interpersonal relationships, and affective regulation. Mathematical models of affect and agent-based models of emotional contagion are well established, but fewer formulations combine a continuous valence–arousal representation, explicit multi-agent coupling, time-continuous interaction dynamics, and mechanically interpretable dynamical parameters within a single framework. Objective This study develops a mathematical and computational model of emotional contagion that integrates intra-individual affective dynamics and inter-individual affective influence within a time-dependent framework based on Russell’s Circumplex Model of Affect. Methods Emotions are modeled as phasors in the complex plane, where each state evolves through the interaction of two oscillators: a radial oscillator for emotional intensity and an angular oscillator for affective direction. Emotional influence among agents is implemented through coupling matrices that allow dynamic simulation of contagion. The full system is expressed as a system of coupled first-order differential equations and solved numerically using Runge–Kutta integration schemes. Results The simulations generated qualitative patterns of phase alignment, persistent state dispersion, leader-induced tracking, oscillatory amplification, and collective convergence under selected parameter and network configurations. They illustrate how attractors, damping, coupling strength, and network topology influence trajectories within the proposed mathematical framework. Conclusion The proposed model offers a theoretically grounded and computationally tractable approach for studying emotional contagion and it should be regarded as an exploratory and hypothesis-generating computational framework. It has not been empirically calibrated or validated as a predictive or neurobiological model of human affective dynamics. Future work should estimate its parameters from empirical affective time series and evaluate its performance using held-out or out-of-sample observations. Nevertheless, the framework opens promising avenues for applications in psychology, affective computing, psychotherapy analytics, and socially intelligent systems.