On predator-prey systems and small-gain theorems

被引:0
|
作者
De Leenheer, P
Angeli, D
Sontag, ED
机构
[1] Univ Florida, Dept Math, Gainesville, FL 32611 USA
[2] Univ Florence, Dipartimento Sistemi & Informat, I-50139 Florence, Italy
[3] Rutgers State Univ, Dept Math, New Brunswick, NJ 08903 USA
关键词
monotone systems; feedback systems; almost global stability; Lotka-Volterra systems;
D O I
暂无
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
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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页码:25 / 42
页数:18
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