A DYNAMICAL LOVE RELATIONSHIP MODEL BETWEEN TWO OPPOSITE GENDERS, INCORPORATING EMOTIONAL DECAY AND INHERENT APPEAL FACTORS

This project employs a dynamical systems approach to model and analyse the longterm behaviour of a romantic relationship, extending the classic Romeo and Juliet model of sentimental dynamics. Beginning with an unstable Basic Model that predicts perpetual emotional oscillation (a Centre equilibrium), the study investigates the impact of crucial psychological factors: emotional decay and inherent appeal. The introduction of the emotional decay factor transforms the system into a Sink, demonstrating that intrinsic self-interest or distraction inevitably leads all initial emotional fluctuations to converge to mutual indifference (the zero equilibrium). This model is solved analytically for and to illustrate varying rates of decay, with complex eigenvalues leading to damped Spiral Sinks and real eigenvalues resulting in direct Nodal Sinks. The final, nonhomogeneous Appeal Model introduces constant appeal terms to account for external relationship sustenance. Analysis shows that while the system remains stable (a Sink), the equilibrium point shifts to a non-zero constant state. This result provides the most robust conclusion: emotional decay ensures that initial romantic volatility fades, but inherent appeal is the necessary factor that sustains the relationship at a stable, long-term level of companionate love, preventing a complete return to indifference. The study confirms that differential equations and phase plane analysis provide a powerful framework for dissecting the stability and asymptotic behaviour of complex sentimental dynamics.