Hering-Breuer Reflex: Phase-Plane Breathing Oscillator

Every breath you take is cut short by a feedback loop you never notice: as the lungs inflate, stretch receptors in the airway walls fire faster and faster, and once their signal — carried by the vagus nerve to the brainstem — crosses a threshold, inspiration is switched off and passive exhalation begins. This 2D companion to the 3D Hering-Breuer simulator keeps the exact same relaxation-oscillator physics but visualizes it the way a physiologist studying an oscillator actually would: as a trajectory through the volume-vs-flow phase plane, where a full breath is not a hidden internal variable but a closed loop you can see, pan and zoom. Drag the inspiratory flow, off-switch threshold, vagal gain and expiratory time constant to reshape the loop in real time, from the slow deep vagotomized cycle (gain = 0) to the small rapid loop typical of a hypersensitive infant reflex (gain ≈ 2×), while a scrolling spirometer strip beneath the plane shows the identical rhythm as a familiar time-domain trace.