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...
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| Format: | Serial |
| Published: |
2016
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| Series: | 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 |
| Summary: | 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. |
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| Physical Description: | 10 |
| ISSN: | 1417-3875 |