When the feasibility of an ecosystem is sufficient for global stability?
We show via a Liapunov function that in every model ecosystem governed by generalized Lotka-Volterra equations, a feasible steady state is globally asymptotically stable if the number of interaction branches equals n-1, where n is the number of species. This means that the representative graph for which the theorem holds is a 'tree' and not only an alimentary chain. Our result is valid also in the case of non-homogeneous systems, which model situations in which input fluxes are present.
Porati
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DBSF-Facolta di Scienze, Universitá dell'Insubria, Varese, Italy. alfredo.porati@unimi.it
Granero
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D000818:Animals; D017753:Ecosystem; D008954:Models, Biological; D011235:Predatory Behavior