Asymptotic behaviour of solutions of Lotka-Volterra systems
Some new sufficient conditions are derived for the competitive exclusion of a few species of a Lotka-Volterra type system of the form \[ \dot x_k=x_k(\beta_{k1}(t)x_1+\dots+\beta_{kn}(t)x_n+\gamma_k(t)), \] where \(\beta_{kj}\) and \(\gamma_k\) are real-valued continuous functions on \(\mathbb R\), \(k,j=1,\dots,n\). The authors also give a proof of the extension of some results of their previous works and establish competitive exclusion of a few species in the system under conditions which are different from those of \textit{F. Montes de Oca} and \textit{M. L. Zeeman} [Math. Anal. Appl. 192, 360--370 (1995; Zbl 0830.34039)]. Conditions for the existence of finite escape times in solutions of the Lotka-Volterra systems and upper-bounds for these times are obtained. The approach is based on results of matrix Riccati equations.
scientific article; zbMATH DE number 5116298