zbMATH — the first resource for mathematics

Periodicity in a “food-limited” population model with toxicants and time delays. (English) Zbl 1025.34070
The paper is devoted to prove the existence of a positive periodic solution to a “food-limited” population model with periodic coefficients and time delay. The proof of the main result is based on degree theory.
Reviewer: Eduardo Liz (Vigo)

34K13 Periodic solutions to functional-differential equations
92D25 Population dynamics (general)
Full Text: DOI
[1] Feng, W., Lu, X.: On diffusive population models with toxicants and time delays. J. Math. Anal. Appl., 233: 373–386 (1999) · Zbl 0927.35049 · doi:10.1006/jmaa.1999.6332
[2] Freedman, H.I., Shukla, J.B.: Models for the effect of toxicant in single species and predator-prey system. J. Math. Biol., 30: 15–30 (1991) · Zbl 0825.92125 · doi:10.1007/BF00168004
[3] Gaines, R.E., Mawhin, J.L.: Coincidence degree and nonlinear differential equations. Springer-Verlag, Berlin, 1977 · Zbl 0339.47031
[4] Gopalsamy, K., He, X., Wen, L.: On a periodic neutral logistic equation. Glasgow Math. J., 33: 281–286 (1991) · Zbl 0737.34050 · doi:10.1017/S001708950000834X
[5] Gopalsamy, K., Kulenovic, M.R.S., Ladas, G.: Environmental periodicity and time delays in a ”food-limited” population model. J. Math. Anal. Appl., 147: 545–555 (1990) · Zbl 0701.92021 · doi:10.1016/0022-247X(90)90369-Q
[6] Gopalsomy, K., Kulenovic, M.R.S., Ladas, G.: Time lags in a ”food-limited” population model. Appl. Anal., 31: 225–237 (1988) · Zbl 0639.34070 · doi:10.1080/00036818808839826
[7] Gopalsomy, K., Zhang, B.G.: On a neutral delay logistic equation. Dyn. Stab. Systems, 2: 183–195 (1988)
[8] Hallam, T.G., Deluna, J.T.: Effects of toxicants on populations: a qualitative approach III. J. Theory Biol., 109: 411–429 (1984) · doi:10.1016/S0022-5193(84)80090-9
[9] Kuang, Y.: Delay differential equations with application in population dynamics, Vol. 191. In: the series of mathematics in science and engineering, Academic Press, Boston, 1993
[10] Li, Y.K.: Positive periodic solution for neutral delay model. Acta Mathematica Sinica, 39(6): 789–795 (1996)
[11] Pielou, E.C.: An introduction to mathematical ecology. Wiley, New York, 1969 · Zbl 0259.92001
[12] Smith, F.E.: Population dynamics in daphnia magna. Ecology, 1963, 44: 651–663 · doi:10.2307/1933011
[13] Zhang, B.G., Gopalsamy, K.: Global attractivity and oscillations in a periodic logistic equation. J. Math. Anal. Appl., 150: 274–283 (1990) · Zbl 0711.34090 · doi:10.1016/0022-247X(90)90213-Y
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.