Two pendulums hanging from the same crossbar gradually begin to swing in sync. But if you give one of them a slight nudge, the shared rhythm changes, and from that change, you can detect even the lightest touch. This is roughly how sensors based on coupled oscillating systems work.
In the new study, the researchers considered two coupled circuits, like two pendulums connected by a spring. Each circuit has an amplifier that sustains the oscillations, but at large amplitudes its gain saturates, like a muscle that tires under heavy strain. The scientists were interested in how such a system behaves near the special point where the frequencies of the two circuits merge into one. There, sensitivity to external influences becomes anomalously high: even a tiny perturbation noticeably shifts the frequency.
However, it turned out that working exactly at this point is difficult: the system becomes unstable, like a pencil balanced on its tip. Therefore, the authors suggest staying nearby, in the region of weak coupling between the circuits. There, sensitivity remains high, but the behavior is predictable. They tested their calculations on two electronic circuits, and the results confirmed that this approach allows building sensors that detect changes invisible to ordinary instruments.
At the point of maximum sensitivity, the system loses stability, like a bicycle that comes to a stop: standing still is nearly impossible, but just next to that point you can ride very slowly while still responding keenly to every pebble.