Dénes Attila and Hatvani László: On the asymptotic behaviour of solutions of an asymptotically Lotka-Volterra model. (2016)
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Abstract
We make more realistic our model [Nonlinear Anal. 73(2010), 650–659] on the coexistence of fishes and plants in Lake Tanganyika. The new model is an asymptotically autonomous system whose limiting equation is a Lotka–Volterra system. We give conditions for the phenomenon that the trajectory of any solution of the original nonautonomous system “rolls up” onto a cycle of the limiting Lotka–Volterra equation as t → ∞, which means that the limit set of the solution of the non-autonomous system coincides with the cycle. A counterexample is constructed showing that the key integral condition on the coefficient function in the original non-autonomous model cannot be dropped. Computer simulations illustrate the results.
| Item Type: | Journal |
|---|---|
| Other title: | Honoring the career of Tibor Krisztin on the occasion of his sixtieth birthday |
| Publication full: | Electronic journal of qualitative theory of differential equations : special edition |
| Date: | 2016 |
| Volume: | 2 |
| Number: | 67 |
| ISSN: | 1417-3875 |
| Number of Pages: | 10 |
| Language: | English |
| DOI: | 10.14232/ejqtde.2016.1.67 |
| Uncontrolled Keywords: | Differenciálegyenlet |
| Additional Information: | Bibliogr.: 10. p. ; összefoglalás angol nyelven |
| Date Deposited: | 2021. Nov. 11. 12:47 |
| Last Modified: | 2021. Nov. 12. 09:42 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/73734 |
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