Small-gain Theorems for Predator-prey Systems

We present a global stability result for Lotka-Volterra systems of the predator-prey type. It turns out that these systems can be interpreted as feedback interconnections of two monotone control systems possessing particular input-output properties. The proof is based on a small-gain theorem, adapted to a setting of systems with multiple equilibrium points. Our main result provides a sufficient condition to rule out oscillatory behavior which often occurs in predator-prey systems.