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Partial survival and extinction in two competing species with impulses. (English) Zbl 1162.34308
Summary: We have considered a nonautonomous two dimensional Lotka-Volterra system with impulsive effect. We prove that one of components will be driven to extinction while the other will stabilize at a certain solution of a impulsive logistic equation under some conditions.

34A34Nonlinear ODE and systems, general
Full Text: DOI
[1] Ahmad, S.: On the nonautonomous Volterra--Lotka competition equations. Proc. amer. Math. soc. 117, 199-204 (1993) · Zbl 0848.34033
[2] Ahmad, S.: Extinction of species in nonautonomous Volterra--Lotka competition systems. Proc. amer. Math. soc. 127, 2905-2910 (1999) · Zbl 0924.34040
[3] Ahmad, S.; Lazer, A. C.: Average conditions for global asymptotic stabity in a nonautonomous Lotka--Volterra system. Nonlinear anal. 40, 37-49 (2000) · Zbl 0955.34041
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[11] De Oca, F. Montes; Vivas, M.: Extinction in a two dimensional Lotka--Volterra system with infinite delay. Nonlinear anal. RWA 7, 1042-1047 (2006) · Zbl 1122.34058
[12] De Oca, F. Montes; Zeeman, M. L.: Extinction in nonautonomous competitive Lotka--Volterra systems. Proc. amer. Math. soc. 124, 3677-3687 (1996) · Zbl 0866.34029
[13] Redheffer, R.: Nonautonomous Lotka--Volterra systems I. J. differential equations 127, 1-20 (1996) · Zbl 0864.34043
[14] Tineo, A.: Necessary and sufficient conditions for extinction of one species. Adv. nonlinear studies 5, No. 1, 57-71 (2005) · Zbl 1091.34028