Dynamic Modeling of Rhythmic Social Systems

This study presents a novel interdisciplinary mathematical framework for modeling Tamburo (drum-based cultural systems) within social–religious environments. The Tamburo is conceptualized as a dynamic signal generator that influences collective human behavior through rhythmic acoustic stimulation. A system of coupled nonlinear differential equations is developed to describe the interactions between social participation, religious engagement, collective synchronization, and emotional resonance. The model captures how rhythmic intensity propagates through a population to enhance coordination and devotion in ritualistic settings. To address uncertainty and qualitative human responses, a socio-fuzzy extension is incorporated, enabling the representation of linguistic variables such as participation levels and devotional states. Furthermore, an agent-based network formulation is introduced to account for interpersonal interactions and localized synchronization effects within crowds. Stability analysis is performed to determine equilibrium states and long-term behavioral patterns under varying rhythmic inputs. The framework is further extended to include nonlinear periodic forcing, fractional-order dynamics, and stochastic perturbations, making it suitable for realistic cultural and social scenarios. Applications of the model include festival dynamics (e.g., Navratri, Garba), temple crowd management, religious psychology, and sound-driven behavioral control mechanisms. The proposed model offers a unique integration of cultural acoustics, applied mathematics, and socio-religious dynamics, providing a new direction for research in computational social science and interdisciplinary modeling.