On Predator-Prey Systems and Small-Gain Theorems - Patrick D. Leenheer; David Angeli; Eduardo D. Sontag (Mathematical Biosciences and Engineering)
This paper deals with an almost global convergence result forLotka-Volterra systems with predator-prey interactions. These systems canbe written as (negative) feedback systems. The subsystems of the feedbackloop are monotone control systems, possessing particular input-outputproperties. We use a small-gain theorem, adapted to a context of systemswith multiple equilibrium points to obtain the desired almost globalconvergence result, which provides sufficient conditions to rule outoscillatory or more complicated behavior that is often observed inpredator-prey systems.