Global attractivity of positive periodic solution to periodic Lotka – Volterra competition systems with pure delay ✩
نویسندگان
چکیده
We consider a periodic Lotka–Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems) ẋi (t)= xi(t) [ ri (t)− n ∑ j=1 aij (t)xj ( t − τij (t) )] , i = 1,2, . . . , n. (∗) We establish some 3/2-type criteria for global attractivity of a positive periodic solution of the system, which generalize the well-known Wright’s 3/2 criteria for the autonomous delay logistic equation, and thereby, address the open problem proposed by both Kuang [Y. Kuang, Global stability in delayed nonautonomous Lotka–Volterra type systems without saturated equilibria, Differential Integral Equations 9 (1996) 557–567] and Teng [Z. Teng, Nonautonomous Lotka–Volterra systems with delays, J. Differential Equations 179 (2002) 538–561]. © 2006 Elsevier Inc. All rights reserved. MSC: primary 34K13; secondary 34K20, 92D25 ✩ Partially supported by NNSF of China (No. 10471153) (X.T., D.C.), by NSERC of Canada and PREA of Ontario. * Corresponding author. E-mail addresses: [email protected] (X.H. Tang), [email protected] (D. Cao), [email protected] (X. Zou). 1 This paper was finalized when X.T. was visiting AMSS, Chinese Academy of Sciences. 2 On leave from Memorial University of Newfoundland. 0022-0396/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jde.2006.06.007 X.H. Tang et al. / J. Differential Equations 228 (2006) 580–610 581
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