A dynamical systems model of emotional contagion: Oscillatory coupling in the circumplex of affect
4 affiliations
- 1Biotechnology Institute, Universidad Nacional de Colombia, Bogotá, Colombia
- 2Research Group in Modelling and Numerical Methods in Engineering - GNUM, Universidad Nacional de Colombia, Bogotá, Colombia
- 3Department of Mechanical and Mechatronics Engineering, Universidad Nacional de Colombia, Bogotá, Colombia
- 4School of Chemical Engineering, University of Birmingham, Birmingham, United Kingdom
Abstract
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.
Related
- Emotional responses to art in situ and on screen: a test of the circumplex model and the genuineness effect.
- State-dependent emergence of coupling between oscillatory and aperiodic neural activity
- Higher-order adaptive behaviors outperform pairwise strategies in mitigating contagion dynamics
- Modelling opinion dynamics during crises as complex contagion with feedback
- Distinct neural oscillatory patterns underlying music-evoked emotions: Evidence from MEG and subjective reports
BibTeX
@article{garzonalvarado2026dynamical,
title = {{A dynamical systems model of emotional contagion: Oscillatory coupling in the circumplex of affect}},
author = {Diego Alexander Garzón-Alvarado and Carlos Alberto Duque-Daza and Alessio Alexiadis and Ricardo Mauricio Tamayo},
journal = {PLOS One},
year = {2026},
month = sep,
doi = {10.1371/journal.pone.0334738},
url = {https://doi.org/10.1371/journal.pone.0334738},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A dynamical systems model of emotional contagion: Oscillatory coupling in the circumplex of affect
AU - Diego Alexander Garzón-Alvarado
AU - Carlos Alberto Duque-Daza
AU - Alessio Alexiadis
AU - Ricardo Mauricio Tamayo
PY - 2026
DA - 2026/09/15
JO - PLOS One
DO - 10.1371/journal.pone.0334738
UR - https://doi.org/10.1371/journal.pone.0334738
AB - 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.
SN - 1932-6203
ER -