= Solution
$T$ is the interval between generations or censuses, and $r$ the prey multiplication without predators. The factor $e^{-aP}$ can be the <probability> of escaping a Poisson number of encounters with mean $aP$, so $a$ <measures> attack intensity. The factor $s$ converts prey resources into predator recruitment, and $b$ modifies the fraction of prey contributing no recruitment. At $b=1$ predators recruit from attacked prey; $b<1$ adds background recruitment, even at $P=0$. A population interpretation valid at every nonnegative state needs $b\le1$, since otherwise the second equation gives negative recruitment near $P=0$.
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