Narrow Results

Through the analysis of a mathematical model we construct in this paper the full catalog of possible love stories among standard (i.e. secure and non-synergic) individuals. For this, we first distinguish between robust and fragile couples, i.e. couples which have one or two stable equilibria. We also distinguish between high and low quality relationships by looking at the sign of the feelings among the partners. Finally, we split fragile couples into two distinct classes, namely those that start from the state of indifference to evolve toward their most desirable equilibrium, as opposed to those that have an unfavorable evolution. The boundaries separating the various classes in any two-dimensional parameter space are either bifurcation curves or special curves characterized by the annihilation of a suitably defined indicator associated to the equilibria or to their basins of attraction. The analysis is performed in part analytically and in part numerically (through continuation methods), and is mainly focused on the role of the appeals of the individuals. The results are in agreement with common wisdom and observations and show, in particular, that love stories can evolve positively even if one of the two individuals has negative feelings in the initial phase of the relationship.

A mathematical model is proposed for interpreting the love story portrayed by Walt Disney in the film "Beauty and The Beast". The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in specific romantic relationships, but also because it enriches the list of examples in which love stories are satisfactorily described through Ordinary Differential Equations.

Micro-macro links between individual psychophysical traits and couple behavior are established. The analysis is carried out through a simple idealized model that mimics couples not influenced by their social environment. The functions describing the traits, i.e. the reactions to the love and appeal of the partner, are quite general. In particular, they allow one to take into account relatively sophisticated characteristics like insecurity and bias. The results are interesting even if some of them have already been discovered in extremely special cases. Some features of the idealized model are also used to theoretically support important behaviors identified empirically by psychotherapists.

We adopt the so-called number representation, originally used in quantum mechanics and recently considered in the description of stock markets, in the analysis of the dynamics of love relation. We present a simple model, involving two actors (Alice and Bob), and we consider either a linear model or a nonlinear model.