La convivencia escolar como sistema dinámico complejo: una propuesta teórica desde la modelización matemática

Humberto Cortés-Peralta; María Jesús Cárdenas-Campos

doi:10.70577/asce.v5i1.657

Authors

Humberto Cortés-Peralta Universidad de Magallanes https://orcid.org/0000-0002-8009-3176
María Jesús Cárdenas-Campos Universidad de Magallanes https://orcid.org/0000-0001-9518-7055

DOI:

https://doi.org/10.70577/asce.v5i1.657

Keywords:

Classroom Environment; Mathematical Models; Social Dynamics; School Climate; Social Interaction

Abstract

School coexistence has traditionally been addressed through approaches focused on individual variables or static descriptions of behavior, which limits the understanding of its collective, nonlinear, and path-dependent dynamics. Therefore, the objective of this study is to propose and analyze a mathematical model based on nonlinear differential equations to conceptualize school coexistence as a complex dynamic system, considering the interaction between the natural drift toward disorder, the intensity of external reinforcements, and the group’s tolerance capacity for order. Consequently, a theoretical study was conducted through the conceptual adaptation of a phase-transition model widely used in dynamical systems theory, which was analyzed by identifying critical points, stability conditions, and bifurcations. The results reveal the existence of critical thresholds and regions of bistability that determine transitions between bad and good behaviour in the classroom, as well as the presence of hysteresis, indicating that classroom dynamics depend on the system’s prior trajectory. It is concluded that school coexistence can be understood as a nonlinear dynamic system in which pedagogical interventions must be sustained, with sufficient intensity to overcome critical thresholds and consolidate stable states of coexistence, providing a conceptual framework to inform the design of more effective pedagogical strategies and future empirical research.

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