Une remarque sur la permanence des systèmes spatialisés

Abstract

The concept of systems is clearly deeply rooted in ecological thinking. However, the importance of space in the interactions within a system is fairly new. In this manuscript, we recall the classical Lotka-Volterra model to model communities of interacting populations, and the historical result by May, linking stability and diversity in randomly connected Lotka-Volterra systems. The concept of permanence is introduced, as well as an interpretation of this result in a case which we hope closer to geographer’s concern, i.e. when the space plays a key role for commanding interactions. We show that restricting interactions between neighbours has a stabilising effect on thr global equilibrium.

Keywords

• dynamic system
• ecology
• spatial interaction
• modeling/modelling
• differential equation
• persistency