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Published on: May 16, 2025
On predator-prey systems and small-gain theorems
Patrick De Leenheer1, David Angeli, Eduardo D Sontag
1Department of Mathematics, University of Florida 411 Little Hall, Gainesville, FL 32611-8105. deleenhe@math.ufl.edu.
Abstract:
This paper deals with an almost global convergence result for Lotka-Volterra systems with predator-prey interactions. These systems can be written as (negative) feedback systems. The subsystems of the feedback loop are monotone control systems, possessing particular input-output properties. We use a small-gain theorem, adapted to a context of systems with multiple equilibrium points to obtain the desired almost global convergence result, which provides sufficient conditions to rule out oscillatory or more complicated behavior that is often observed in predator-prey systems.
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