Stability conditions for two predator one prey systems (Q1119208)

The authors study the problem of generalizing the Rosenzweig-MacArthur ``graphical criterion'' of stability from a one-prey one-predator to a one-prey two-predator system. They show that in general, the criterion cannot be generalized, but that in the case of no interspecific competition between predators, it can be. They also show that in the case of no intraspecific competition at one of the predators an Andronov-Hopf bifurcation occurs. Finally, they are able to give sufficient conditions for global asymptotic stability in a specific case of interest in the applications. The proofs will appear elsewhere.