Exploring the Dynamics of Romantic Relationships Through the Lens of Prem Rog

Romantic relationships are dynamic events that begin, grow, and frequently remain for a long time in a stagnant or fluctuating state until possibly dissipating. Although they are unquestionably the most significant dynamic events in our lives, dynamic systems theory has only recently included them in its formal framework. Without a mathematical model, it would be impossible to analyze and comprehend the dynamics because, in general, love stories are too brief to allow things to stabilize and are affected by the ups and downs of the surrounding community. In this paper, we set up models made up of four ordinary differential equations to represent the dynamics of the feelings of the three main characters in the Hindi-language film Prem Rog to illustrate the effectiveness of this modeling approach. The study also employs graphical representation to trace the narrative for which the model is analyzed. Experiments using this model approach, along with several simulations, provide fascinating studies that examine various love dynamics, including attraction, distaste, and neglect, as well as model stability. The analysis illustrates how behavioral factors influence the quality of romantic relationships and how individual appeal contributes to order within a social system.