Layla and Majnun: A Complex Love Story

Following previous work, this paper introduces a new dynamical model involving two differential equations describing the time variation of behavior displayed by a couple in a romantic relationship. This model is different from previous ones because it uses complex variables. Since complex variables have both magnitude and phase, they are better able to represent love and can represent more complex emotions such as coexisting love and hate. The model treats feelings as a two-dimensional vector rather than a scalar, which is a step closer to reality. Another interesting characteristic of the new model is its ability to show transiently chaotic behavior between only two individuals, which in previous models appeared only in love triangles. The sensitive dependence on initial conditions represents the unpredictable dynamics of love affairs.