Partial persistence and extinction in \(N\)-dimensional competitive systems
The authors study an N-dimensional system lightly more general than a Lotka-Volterra system. It has the form \[ u_k'(t)=u_k(t)\left[a_k(t)-\sum_{l=1}^N b_{kl}u_l(t)\right],\quad k=1,\dots,N, \] with \(b_{kl}\geq 0,\;b_{kk}>0,\;1\leq k,l,\leq N. \) Conditions for strong persistence of all species are derived. Here, computable conditions are given on the coefficients which imply the ultimate extinction of certain species in an \(N\)-dimensional Lotka-Volterra system.
scientific article; zbMATH DE number 2136690
scientific article