= Event-triggered harvesting by conserved energy
{title2=$\Delta H=-ch-d\log(1-h/X)$}
The predator-prey <first integral> $H=cX-d\log X+bY-a\log Y$ changes by the displayed amount when $h$ prey are removed. At a fixed prey threshold this increment is constant; sufficiently high thresholds reduce oscillation energy until the threshold is no longer crossed. At a fixed predator threshold, the increment depends on the prey abundance and on the crossing direction. A rising-predator balanced-quota cycle has negative return multiplier of magnitude greater than one; its leading small-oscillation approximation is marginal rather than a robust attractor.
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