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Periodic solutions for a prey-predator differential delay equation. (English) Zbl 0365.34078


MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C25 Periodic solutions to ordinary differential equations
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References:

[1] Grafton, R., A periodicity theorem for autonomous functional differential equations, J. Differential Equations, 6, 87-109 (1969) · Zbl 0175.38503
[2] Hale, J. K., Functional Differential Equations (1971), Springer-Verlag: Springer-Verlag New York · Zbl 0213.36901
[3] Hirsh, M.; Smale, S., Differential Equations, Dynamical Systems and Linear Algebra, ((1974), Academic Press: Academic Press New York), 255-275 · Zbl 0309.34001
[4] Jones, G., The existence of periodic solutions of \(f\)′\((x)\) = −\( αf (x\) − 1){\(1 + f(x)\)}, J. Math. Anal. Appl., 5, 435-450 (1962) · Zbl 0106.29504
[5] Leung, A.; Wang, A., Analysis of models for commercial fishing: mathematical and economical aspects, Econometrica, 44, 295-303 (1976) · Zbl 0319.90017
[6] Leung, A., Limiting behaviour for several interacting populations, Math. Biosci., 29, 85-98 (1976) · Zbl 0335.92020
[7] Wangersky, P.; Cunningham, W., Time lag in prey predator population models, Ecology, 38, 136-139 (1957)
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