= Leslie-Gower predator-prey model
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The system $\dot u=u(1-u)-auv/(u+d)$, $\dot v=bv(1-v/u)$ combines logistic prey growth, saturating predation and a predator carrying level proportional to prey density. Its unique positive equilibrium is $u=v=s$, where $(1-s)(s+d)=as$. Its <Jacobian matrix> has <determinant> $bs\sqrt{(1-a-d)^2+4d}/(s+d)>0$ and trace $s(1-d-2s)/(s+d)-b$. The <positive trapping construction for the Leslie-Gower model> gives a compact positive region and a <limit cycle> whenever this equilibrium is a repeller.
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