Hu, Hongxiao; Teng, Zhidong; Jiang, Haijun On the permanence in non-autonomous Lotka-Volterra competitive system with pure-delays and feedback controls. (English) Zbl 1169.93011 Nonlinear Anal., Real World Appl. 10, No. 3, 1803-1815 (2009). Summary: This paper,which is a continuation of [H. Hu, Z. Teng and H. Jiang, On the extinction in nonautonomous Lotka-Volterra competitive system with pure-delays and feedback controls, Appl. Math. Comput. (2007) (submitted for publication)], considers general \(n\)-species non-autonomous Lotka-Volterra competitive systems with pure-delays and feedback controls. New sufficient conditions for which a part of the \(n\) species remains permanent, are established by applying the method of multiple Lyapunov functionals and introducing a new analysis technique. In contrast to previous works (see, for example, references [F. Chen, Nonlinear Anal., Real World Appl. 7, No. 1, 133–143 (2006; Zbl 1103.34038); Appl. Math. Comput. 178, No. 2, 474–479 (2006; Zbl 1101.92035); Appl. Math. Comput. 173, No. 2, 694–709 (2006; Zbl 1087.92059); F. Chen, Z. Li, Zhong and Y. Huang, Nonlinear Anal., Real World Appl. 8, No. 2, 680–687 (2007; Zbl 1152.34366)]), we introduce a new research method and obtain feedback controls that can not influence the permanence of species. Cited in 29 Documents MSC: 93B52 Feedback control 93C23 Control/observation systems governed by functional-differential equations 45D05 Volterra integral equations Keywords:non-autonomous Lotka-Volterra system; competition; extinction; permanence; feedback control; pure-delay Citations:Zbl 1103.34038; Zbl 1101.92035; Zbl 1087.92059; Zbl 1152.34366 PDFBibTeX XMLCite \textit{H. Hu} et al., Nonlinear Anal., Real World Appl. 10, No. 3, 1803--1815 (2009; Zbl 1169.93011) Full Text: DOI References: [1] Cao, Y.; Gard, T. 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