(untitled) (Selecciones Matemáticas, 2025)
This work interprets human conversation as a controllable and observable dynamical system. Each interlocutor influences the discursive state of the other, allowing the interaction to be modeled by differential equations. Using results from control theory, we consider a convex and compact space as admissible interactions, with extreme points corresponding to bang–bang interventions such as interruptions or emphatic statements. We validate the model through numerical simulations and synchrony metrics, showing that conversational symmetry improves stability and consensus, asymmetry produces biased equilibria, and temporal variations in coupling generate transient desynchronization followed by recovery, analogous to conflict and reconciliation phases in dialogue.