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On the permanence in non-autonomous Lotka-Volterra competitive system with pure-delays and feedback controls. (English) Zbl 1169.93011
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.
MSC:
93B52Feedback control
93C23Systems governed by functional-differential equations
45D05Volterra integral equations