Equilibria in systems of interacting structured populations
The existence of a stable positive equilibrium density for a community of k interacting structured species is studied as a bifurcation problem. Under the assumption that a subcommunity of k-1 species has a positive equilibrium and under only very mild restrictions on the density dependent vital growth rates, it is shown that a global continuum of equilibria for the full community bifurcates from the subcommunity equilibrium at a unique critical value of a certain inherent birth modulus for the k th species. Local stability is shown to depend upon the direction of the bifurcation. The direction of bifurcation is studied in more detail for the case when vital per unit birth and death rates depend upon population density through positive linear functionals of density and for the important case of two interacting species.
existence of a stable positive equilibrium density
scientific article; zbMATH DE number 4035631
scientific article