= Annual pulse-breeding predator-prey model
{title2=$X'=rXe^{-\kappa Y},\quad Y'=sY(1+bX')$}
An <annual pulse-breeding predator-prey model> combines continuous <predation> and mortality between short reproduction episodes with an annual <difference equation>. If surviving <predators> produce offspring in proportion to <prey> surviving the year, retained adults give the displayed map. Here $r$ combines <prey> reproduction and natural survival, $s$ is <predator> survival, and $\kappa$ integrates <predation> over declining <predator> abundance. The positive annual <equilibrium> is $X_*=(1-s)/(sb)$, $Y_*=\log r/\kappa$ for $r>1$ and $0<s<1$.
Back to article page
