Permanence and periodic solution in competitive system with feedback controls. (English) Zbl 0896.92032

Summary: Sufficient conditions are derived for the permanence and existence of global asymptotical stability in a two species competitive system with feedback controls. It is shown that the controls can save extinction of the species.


92D40 Ecology
93B52 Feedback control
92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations
93D15 Stabilization of systems by feedback
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[1] Ahmad, S., Convergence and ultimate bounds of the nonautonomous Volterra-Lotka competition equation, J. Math. Anal. Appl., 127, 377-387 (1987) · Zbl 0648.34037
[2] Ahamd, S., On the nonautonomous Volterra-Lotka competition equations, J. Math. Anal. Appl., 117, 199-204 (1993) · Zbl 0848.34033
[3] Zeng, G. Z.; Chen, L. S.; Chen, J. F., Persistence and periodic orbits for two-species nonautonomous diffusion Lotka-Volterra models, Mathl. Comput. Modelling, 20, 2, 69-80 (1994) · Zbl 0827.34040
[4] Alvarez, C.; Lazer, A. C., An application of topological degree to the periodic competing species problem, J. Austral. Math. Soc. Ser. B., 28, 202-219 (1986) · Zbl 0625.92018
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