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On species extinction in an autonomous competition model. (English) Zbl 0846.34043
Lakshmikantham, V. (ed.), World congress of nonlinear analysts ’92. Proceedings of the first world congress, Tampa, FL, USA, August 19-26, 1992. 4 volumes. Berlin: de Gruyter. 359-368 (1996).
Summary: We study an autonomous \(N\)th order Lotka-Volterra system of differential equations. It is shown that if the coefficients satisfy certain inequalities, then given a solution with positive initial values, the \(N\)th component of such a solution approaches zero while the rest approach a certain solution of a smaller system.
For the entire collection see [Zbl 0836.00032].

34D05 Asymptotic properties of solutions to ordinary differential equations
92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations