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Carrillo, J.A., Fornasier, M., Toscani, G. and Vecil, F. (2010) Particle, Kinetic, and Hydrodynamic Models of Swarming. In: Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, 297-336.
https://doi.org/10.1007/978-0-8176-4946-3_12

has been cited by the following article:

• TITLE: Propagation of Emotions and Attitudes in Football

  AUTHORS: Mamadou Moustapha Diop, Aliou Sonko

  KEYWORDS: Emotional Propagation, Reaction-Diffusion Equation, Football Tactics, Collective Behavior, Mathematical Modeling

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.1, January 27, 2026

  ABSTRACT: This article proposes a hybrid model to study the propagation of collective and individual emotions within a football team. The model combines a reaction-diffusion equation to describe the spatial dynamics of emotions on the field and a system of coupled differential equations to capture psychosocial interactions between players. We demonstrate the existence and uniqueness of the solutions using the Lax-Milgram theorem (for the partial differential equation) and the Cauchy-Lipschitz theorem (for the ordinary differential equations). This theoretical framework unifies, for the first time, the emotional and tactical aspects of football, offering perspectives for real-time analysis of team performance.