On the asymptotic behaviour of solutions of an asymptotically Lotka-Volterra model
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 s...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2016
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| Sorozat: | Electronic journal of qualitative theory of differential equations : special edition
2 No. 67 |
| Kulcsszavak: | Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2016.1.67 |
| Online Access: | http://acta.bibl.u-szeged.hu/73734 |
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| 024 | 7 | |a 10.14232/ejqtde.2016.1.67 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Dénes Attila | |
| 245 | 1 | 3 | |a On the asymptotic behaviour of solutions of an asymptotically Lotka-Volterra model |h [elektronikus dokumentum] / |c Dénes Attila |
| 260 | |c 2016 | ||
| 300 | |a 10 | ||
| 490 | 0 | |a Electronic journal of qualitative theory of differential equations : special edition |v 2 No. 67 | |
| 520 | 3 | |a 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. | |
| 695 | |a Differenciálegyenlet | ||
| 700 | 0 | 1 | |a Hatvani László |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/73734/1/ejqtde_spec_002_2016_067.pdf |z Dokumentum-elérés |