 Annual pulse-breeding predator-prey model

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 $X_{\ast }=(1-s)/(sb)$, $Y_{\ast }=\log r/\kappa$ for $r>1$ and $0<s<1$.