title: Coexistence and survival in conservative Lotka-Volterra networks.
abstract: Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network's interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time.
authors.affiliation: Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany.
authors.forename: Johannes
authors.initials: J
authors.lastname: Knebel
authors.forename: Torben
authors.initials: T
authors.lastname: Krüger
authors.forename: Markus F
authors.initials: MF
authors.lastname: Weber
authors.forename: Erwin
authors.initials: E
authors.lastname: Frey
mesh_terms: D018533:Biomass; D017753:Ecosystem; D053476:Extinction, Biological; D008954:Models, Biological; D011157:Population Dynamics