Cyclic Dynamics in Romantic Relationships

Minimal models composed of two ordinary differential equations are considered in this paper to mimic the dynamics of the feelings between two persons. In accordance with attachment theory, individuals are divided into secure and non-secure individuals, and synergic and non-synergic individuals, for a total of four different classes. Then, it is shown that couples composed of secure individuals, as well as those composed of non-synergic individuals can only have stationary modes of behavior. By contrast, couples composed of a secure and synergic individual and a non-secure and non-synergic individual can experience cyclic dynamics. In other words, the coexistence of insecurity and synergism in the couple is the minimum ingredient for cyclic love dynamics. The result is obtained through a detailed local and global bifurcation analysis of the model. Supercritical Hopf, fold and homoclinic bifurcation curves are numerically detected around a Bogdanov–Takens codimension-2 bifurcation point. The existence of a codimension-2 homoclinic bifurcation is also ascertained. The bifurcation structure allows one to identify the role played by individual synergism and reactiveness to partners love and appeal. It also explains why ageing has a stabilizing effect on the dynamics of the feelings. All results are in agreement with common wisdom on the argument. Possible extensions are briefly discussed at the end of the paper.