Modeling love: Understanding the dynamics of human relationships

Is it possible to predict how love affairs will develop using mathematical models? According to the book Modeling Love Dynamics by researchers from the IIASA Evolution and Ecology Program and colleagues, the simple answer is yes. The message from the research is that prediction is possible, if the way each individual reacts to the love and appeal of their partner can be described in formulas.

Consider a standard love story, which develops like those described in a classic Hollywood movie such as “Titanic.” This story can be modeled by considering appealing individuals who increase their own love as their partner’s increases—so called secure individuals. Starting from the state of indifference, where the individuals are at their first encounter, their feelings continuously grow and tend toward a positive plateau.

Love stories become more intriguing when one individual is not particularly appealing, if not repellant, as in the fairy tale “Beauty and The Beast.” In these cases, there is a second romantic regime, which can lead to marital dissolution in the long run. In order to avoid that trap, people who are not very charming do all they can to look more attractive to the partner at first. After a while, the bluffing can stop, because the couple has entered the safe basin of attraction.

Not all individuals are secure. Indeed, some people react less strongly when the love of their partner exceeds a certain threshold. These individuals, often very keen on flirtation, are less capable of becoming one with their partner. The model shows that couples composed of insecure individuals tend, with almost no exception, toward an unbalanced romantic regime in which the most insecure is only marginally involved and is therefore prone to break up the relationship at the first opportunity. This is illustrated by the characters Scarlett O’Hara and Rhett Butler in the famous film “Gone with the Wind”.

Mathematical models can also be used to interpret more complex romantic behaviors. Take the case of “biased” individuals who overestimate the appeal of their partners when they are more in love with them. Interestingly, if insecurity is also present, biased couples can have romantic regimes characterized by recurrent ups and downs. In other words, bias and insecurity is an explosive mix that makes for a turbulent relationship.

The second part of the book focuses on the effects of the social environment. In this context, the researchers analyze the 20-year relationship between the famous Italian poet Francis Petrarch and a woman known only as “Laura,” showing that poetic inspiration is an important destabilizing factor, responsible for transforming a quiet relationship into a turbulent one.

Finally, the team studied triangular relationships, with emphasis on the effects of conflict and jealousy. In these cases, the dynamics of feelings can be very wild, up to the point of being chaotic and, hence, unpredictable. When this occurs, the life of the couple becomes unsustainable, because painful periods of crisis can start at virtually any moment: a heavy permanent stress.

Example of how complex human relationships can be understood as dynamical systems. The illustration refers to “Gone with the Wind”, one of the most popular films of all time. The red and blue lines, respectively, show the time evolution of Scarlett O’Hara’s and Rhett Butler’s involvements during their love story, as predicted by the mathematical model by Rinaldi et al. [1].


[1] Rinaldi S, Della Rossa F, Dercole F, Gragnani A & Landi P (2016). Modeling Love Dynamics. World Scientific, Singapore.


  • Department of Electronics and Information, Politecnico di Milano, Italy