Peng, Qiuliang; Chen, Lan-Sun Asymptotic behavior of the nonautonomous two-species Lotka-Volterra competition models. (English) Zbl 0798.92023 Comput. Math. Appl. 27, No. 12, 53-60 (1994). Summary: Nonautonomous two-species Lotka-Volterra competition models are considered, where all the parameters are time-dependent and asymptotically approach periodic functions, respectively. Under some conditions, it is shown that any positive solutions of the models asymptotically approach the unique strictly positive periodic solution of the corresponding periodic system. Cited in 2 ReviewsCited in 9 Documents MSC: 92D25 Population dynamics (general) 34E99 Asymptotic theory for ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations 34C25 Periodic solutions to ordinary differential equations Keywords:nonautonomous two-species Lotka-Volterra competition models; global asymptotic stability; comparison theorem; positive solutions PDFBibTeX XMLCite \textit{Q. Peng} and \textit{L.-S. Chen}, Comput. Math. Appl. 27, No. 12, 53--60 (1994; Zbl 0798.92023) Full Text: DOI References: [1] Smith, J. M., Mathematical Ideas in Biology (1968), Cambridge Univ. Press: Cambridge Univ. Press London [2] Gopalsamy, K., Exchange of equilibria in two species Lotka-Volterra competition models, J. Austral. Math. Soc. Ser., B24, 160-170 (1982) · Zbl 0498.92016 [3] Ahmal, S., Convergence and ultimate bounds of solutions of the nonautonomous Volterra-Lotka competition equations, J. Math. Anal. & Appl., 127, 377-387 (1987) [4] Alvarez, C.; Lazer, A. C., An application of topological degree to the periodic competing species problem, J. Austral. Math. Soc. Ser., B28, 202-219 (1986) · Zbl 0625.92018 [5] Massera, J. L., The existence of periodic solutions of systems of differential equations, Duke Math. J., 17, 457-475 (1950) · Zbl 0038.25002 [6] Freedman, H. I.; Sree Hari Rao, V.; So, J. W.-H., Asymptotic behavior of a time-dependent single-species model, Analysis, 9, 217-223 (1989) · Zbl 0678.34056 [7] Coddington, E. A.; Levinson, N., Theory of Ordinary Differential Equations (1955), McGraw-Hill: McGraw-Hill New York · Zbl 0042.32602 [8] Chen, L.-S., Mathematical Models and Methods in Ecology (1988), Science Press: Science Press Beijing, (in Chinese) [9] Freedman, H. I., Deterministic Mathematical Models in Population Ecology (1980), Marcel Dekber: Marcel Dekber New York · Zbl 0448.92023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.