Nonautonomous Lotka-Volterra systems with delays. (English) Zbl 1013.34072
The author studies a general nonautonomous Lotka-Volterra-type system with delays. A series of sufficient conditions for the ultimate boundedness, permanence, global attractivity, and existence and uniqueness of strictly positive solutions, positive periodic solutions, and almost-periodic solutions are established. These are extensions of results due to R. Redheffer [J. Differ. Equations 127, No. 2, 519-541 (1996; Zbl 0856.34056) and ibid. 132, No. 1, 1-20 (1996; Zbl 0864.34043)] given for the corresponding system without delays.
Reviewer: Tibor Krisztin (Szeged)
MSC:
| 34K14 | Almost and pseudo-almost periodic solutions to functional-differential equations |
| 92D25 | Population dynamics (general) |
| 34K12 | Growth, boundedness, comparison of solutions to functional-differential equations |
| 34K13 | Periodic solutions to functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
Keywords:
nonautonomous Lotka-Volterra system; delay; global attractivity; strictly positive solution; periodic solution; almost-periodic solution; permanenceReferences:
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