Scientists Found A Mathematical Formula For Why Some Relationships Last And It All Comes Down To One Threshold

Professor Laurent Pujo-Menjouet of the University of Lyon I has spent decades applying mathematical modeling to one of the questions that resists quantification most stubbornly: why do some relationships survive the inevitable stresses of a shared life while others slowly fall apart? His book, Love! Valour! Equations!, synthesizes decades of research from multiple fields, including work by psychologist John Gottman, economist José Manuel Rey, physicist Sergio Rinaldi, and mathematician Steven Strogatz, who was among the first to apply dynamical systems theory to romantic relationships. The framework treats a relationship the way population ecologists treat an animal group: feelings evolve over time in response to outside pressures, and the system either returns to a stable state after disruption or tips past a threshold from which recovery becomes increasingly unlikely. The concept of a critical threshold, borrowed from a population ecology idea called the Allee effect, is the central finding: each relationship appears to have a minimum level of emotional connection below which decline becomes mathematically probable. Pujo-Menjouet is direct about what this means in practical terms. If your feelings fall below this threshold and stay there, the mathematics predicts an inevitable decline toward separation. Understanding the threshold, he says, gives couples a powerful tool: they can recognize danger zones and take corrective action before the mathematics catches up with them.

The model Pujo-Menjouet and his colleagues have developed identifies three major forces that shape whether a relationship remains stable over time. The first is the mutual attraction between the partners. The second is the natural weakening of emotional intensity that can occur across years together. The third is how each person responds to the other emotionally, which the model treats not as fixed but as something that can be trained, improved, and actively managed. Polish researchers who extended the model added a fourth element worth noting: the role of delayed reactions in conflict, meaning how long a person waits before responding to a disagreement can either calm the situation or make it worse, with short reaction times in heated arguments tending to escalate conflict. The key question the model asks of any couple is not whether stress or conflict occurs, which is mathematically assumed as inevitable, but how effectively the couple rebounds from those disruptions afterward. Pujo-Menjouet describes this resilience using the Three Little Pigs: life will always send its wolves, including stress, illness, work, children, and financial difficulties, and the mathematics helps you understand how to build the brick house rather than the straw one. He was careful to note the model's limits: most of the data comes from Western relationships, human behavior does not always follow predictable rules, and people can change in ways no equation can fully anticipate. The equations are meant to identify tendencies, not predict an unavoidable future. Success, he says, still depends on two people choosing every day to nurture their connection. The equations can show you the path. You still have to walk it together.

Source:https://www.sciencedaily.com/releases/2026/09/260906170140.htm