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Some new results on the permanence and extinction of nonautonomous Gilpin-Ayala type competition model with delays. (English) Zbl 1120.34062
Mainly stimulated by the works of Z. Teng and Y. Yu [J. Math. Anal. Appl. 241, 254–275 (2000; Zbl 0947.34066)], and M. Fan and K. Wang [Comput. Math. Appl. 40, No. 10–11, 1141–1151 (2000; Zbl 0954.92027)], the author proposes a delayed nonautonomous \(n\)-species Gilpin-Ayala type competitive system. By using differential inequality technique, a set of sufficient conditions are established under which a part of the \(n\) species of the system are driven to extinction while the remaining part are uniformly persistent.

MSC:
34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics (general)
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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