Propagation of Emotions and Attitudes in Football

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.