When two systems interact, they often produce feedback loops.

A feedback loop arises when some property of the first system governs some property of the second system while, at the same time, the second property governs the first property, with some delay. Expressed as numeric values, we can plot these properties as functions of time and even describe them in the form of a differential equation and predict outcomes.

Now imagine that the two systems in question represent two persons in a relationship and the two variables regulating one another represent their emotional states. If we could measure the degree of influence of one partner’s emotions on those of the other, we could express the dynamics of their relationship as a differential equation. If we do so with sufficient accuracy, the differential equation could then predict the couple’s mood and attitude fluctuations toward one another.

Mathematics of marriage: dynamic nonlinear models provides the tools for analysis and prediction of the behavior of such nonlinear dynamic systems.

How can these formulas predict divorce or a similar breakdown of a human relationship?

Catastrophic instability arises from unchecked positive feedback. Despite its rather upbeat name, positive feedback usually spells trouble: it arises when a change in the value of a variable causes further proportional change in the same direction. For example, A experiences anger, which causes B to experience more anger, which causes A to experience more anger yet, and so forth until the system disintegrates. Nuclear fission serves as another example of positive feedback leading to catastrophic meltdowns or explosions.

What does nonlinear mean? In a nonlinear system, a change of the value of a variable will produce different effects depending on the current state of the dependent variable. For example, person B in a good mood might not experience the same jolt of anger in response to A’s angry diatribe as she would when in a neutral mood.

Nonlinear dynamics require more sophisticated mathematical tools than linear systems. Still, they only approximate the full dynamics of a relationship which must have a myriad of nonlinearly dependent variables.

Stranger yet, these variables seem to lie outside of our conscious control or even awareness. In “A General Theory of Love” the authors (three practicing psychotherapists) lay out their understanding of love as stable mutual regulation of limbic systems of mammals. The limbic system of the mammalian brain governs the animal’s emotional states, affect, and motivation. Through mostly nonconscious expressions of emotion, limbic systems of two mammals influence one another. Thus, mammals can often communicate across species thanks to their similar wiring: polar bears play with huskies and your dog understands perfectly how you feel at the end of the day and his elation shines through to your perception at the smallest hint of affection or playfulness.

The authors define love as “finding someone who regulates you well and staying with them.”

These musings don’t qualify as science yet, but they hint at a direction. We can make many falsifiable hypotheses and design specific experiments to test them.