Extinction in nonautonomous \(T\)-periodic competitive Lotka-Volterra system. (English) Zbl 0906.92024
Summary: A nonautonomous \(T\)-periodic competitive Lotka-Volterra system of \(n\) species is considered. It is shown that if the coefficients are \(T\)-periodic, continuous and satisfy certain inequalities, then any solution with strictly positive initial conditions has the property that all but one of its components vanish while the remaining component approaches the canonical solution of a certain logistic differential equation.
MSC:
| 92D25 | Population dynamics (general) |
| 34C99 | Qualitative theory for ordinary differential equations |
| 34C25 | Periodic solutions to ordinary differential equations |
References:
| [1] | Montes de Oca, F.; Zeeman, M. L., Extinction in nonautonomous competitive Lotka-Volterra systems, (Proc. Amer. Math. Soc., 124 (1996)), 3677-3687 · Zbl 0866.34029 |
| [2] | Ahmad, S., On the nonautonomous Volterra-Lotka competition equations, (Proc. Amer. Math. Soc., 117 (1993)), 199-205 · Zbl 0848.34033 |
| [3] | Ahmad, S.; Lazer, A. C., One species extinction in an autonomous competition model, (Proceedings of the World Congress on Nonlinear Analysis (1996), Walter de Gruyter: Walter de Gruyter Berlin-NY) · Zbl 0846.34043 |
| [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 |
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