On Predator-Prey Systems and Small-Gain Theorems
Open Access
- 1 January 2005
- journal article
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Biosciences and Engineering
- Vol. 2 (1) , 25-42
- https://doi.org/10.3934/mbe.2005.2.25
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.Keywords
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