Is there a formula for lasting love? Researchers who have studied romantic relationships for decades believe that emotional changes often follow recognizable patterns—and that mathematical models can help explain why some couples remain stable while others drift apart.
Professor Laurent Pujo-Menjouet of the University of Lyon 1 and researchers around the world have developed mathematical models that treat romantic relationships as dynamical systems. This approach examines how emotions evolve, respond to stress, and recover—or decline—over time.
In his book Love! Courage! Equation!, a work combining mathematics, psychology, literature, film, and everyday life, Pujo-Menjouet writes: “There is no mystical magic or magic potion. Now you know that. Is all hope lost then? Of course not. That’s exactly where it all gets interesting.”
From population models to romantic relationships
The mathematical study of relationship stability begins in an unexpected place: the animal kingdom.
Some of the theories now being applied to romantic relationships were originally developed to understand changes in animal populations. Malthusian models and predator-prey equations, for example, have been used to study the spread of Australian rabbits and fluctuations in Canadian lynx and snowshoe hare populations.
Another important concept is the Allee effect, which describes what happens when a population falls below a critical level. Once that threshold is crossed, survival becomes more difficult. Above it, the population is more likely to grow and remain stable.
Researchers have found that a similar threshold can help explain the stability of romantic relationships.
“Just as we can model population growth or the decline of endangered species, we can model the evolution of emotions within couples,” explains Pujo-Menjouet. “We’re not trying to predict who you’ll fall in love with. We’re trying to understand why, despite life’s inevitable shocks, some couples remain stable while others slowly drift apart.”
This approach builds on a long history of mathematical research, including Thomas Malthus’ population model from the 18th century, the Lotka-Volterra predator-prey equations developed in the 1920s, and later work by psychologist John Gottman, economist José Manuel Rey, physicist Sergio Rinaldi, and mathematician Stephen Strogatz. Strogatz was among the first researchers to apply dynamical systems theory directly to romantic relationships.
The mathematical threshold for a stable relationship
Psychologist Dr. John Gottman, often referred to as “Dr. Love,” helped demonstrate that interpersonal behavior can be studied mathematically. By coding couples’ interactions and converting their behavior into graphs, researchers can use mathematical models to identify patterns linked to relationship outcomes.
More recent approaches add another layer of complexity: delayed reactions. Introduced in relationship modeling by researchers including Bielezik, Follis, and Marek Bodnar, this concept recognizes that people do not always respond immediately during disagreements. The time someone takes to react, reflect, or communicate can either calm a conflict or make it worse.
Despite the growing sophistication of these models, one central idea remains relatively simple, says Pujo-Menjouet. Every relationship may have a critical threshold representing the minimum level of emotional connection needed to keep the bond stable.
“If your emotions fall below this threshold and remain there, the mathematics predicts an inevitable decline toward separation,” says Pujo-Menjouet. “But understanding this threshold gives couples a powerful tool: the ability to recognize warning signs and take corrective action.”
His team has also developed models that account for everyday disruptions, including stress, arguments, illness, work demands, and financial pressure. The key question is not whether these challenges occur, but how effectively couples recover from them.
“The important question is not whether couples argue,” says Pujo-Menjouet. “The question is whether they are resilient enough to return to equilibrium afterward.”
Three forces that shape long-term love
The relationship model highlights three major factors that influence whether a couple remains stable over time.
The first is mutual attraction between partners. The second is the gradual weakening of emotions that can naturally occur over time. The third is the way each person responds emotionally to the other.
Together, these forces help determine how resilient a relationship will be when it faces stress, conflict, and major life changes.
Pujo-Menjouet compares this resilience to the story of the three little pigs. “There are always wolves in life: stress, illness, work, children, and financial difficulties. Mathematics helps us understand how to build a brick house instead of a straw house.”
Could AI become an early warning system for relationships?
Researchers are also exploring how mathematical relationship models could be combined with artificial intelligence. One potential application is an AI-powered early warning system for couples.
Such a system could identify signs that a relationship is becoming unstable and alert partners early enough to change direction. It could potentially highlight recurring conflict patterns, emotional distance, or difficulties recovering after disagreements.
Pujo-Menjouet says this technology could give partners valuable “time to correct course.”
“Think of it as the GPS of relationships,” says Pujo-Menjouet. “It shows you where you are, where you are going, and suggests routes to reach your desired destination. Rather than telling you who to love, the model helps explain how love evolves and what couples can do to protect it.”
Why love cannot be reduced to an equation
Researchers also emphasize that mathematical models of love have important limitations.
Many existing models are based primarily on patterns observed in Western relationships. The reasons couples succeed or separate can vary significantly according to culture, religion, socioeconomic status, family structure, and generation. Developing a model that applies universally would require far more complex research.
Human behavior is also not always predictable. People can act irrationally, change their habits, seek therapy, deepen their commitment, and grow in ways that mathematical models cannot fully anticipate.
For that reason, relationship equations are designed to identify trends rather than predict an unavoidable future. Couples can still make choices that challenge what a model suggests.
“Mathematics can reveal patterns and provide guidance,” explains Pujo-Menjouet. “But ultimately, the success of a relationship depends on the choices two people make each day to nurture their bond. The equation shows the way, but you still have to walk it together.”
Source: www.sciencedaily.com