A Criterion of Global Convergence to Equilibrium for Differential Systems with an Application to Lotka-Volterra Systems
| Citations: | 4 - 1 self |
BibTeX
@MISC{Gouze_acriterion,
author = {Jean-Luc Gouze},
title = {A Criterion of Global Convergence to Equilibrium for Differential Systems with an Application to Lotka-Volterra Systems},
year = {}
}
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Abstract
this paper, we show that it is sometimes possible to describe in a simple way some of the global features of (1).We shall give sucient conditions which ensure the existence of an equilibrium in a given region in R , and a global convergence in this region towards the equilibrium. The key idea in our study of system (1) in R is to immerse it into a cooperative system in R , where it is possible to obtain an upper and a lower bound on the solution of (1). Of course the condition obtained is conservative and puts strong constraints on the system (1). We explain this in section 4
