×

The effects of a single stage-structured population model with impulsive toxin input and time delays in a polluted environment. (English) Zbl 1187.34118

In this paper, the authors consider the dynamics of a single stage-structured population model with impulsive toxin input and time delays (including constant individual maturation time delay and pollution time delay) in a polluted environment, in which the authors assume that only the mature individuals are affected by pollutants. The conditions for the global attractivity of the population-extinction periodic solution and the permanence of the population are obtained. The authors show that maturation time delay and impulsive toxin input can bring great effects on the dynamics of the system, and pollution time delay is harmless. Numerical simulations confirm the theoretical results.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K45 Functional-differential equations with impulses
92D40 Ecology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hallam TG, J. Math. Biol. 18 pp 25– (1983)
[2] DOI: 10.1016/0304-3800(83)90019-4 · doi:10.1016/0304-3800(83)90019-4
[3] DOI: 10.1142/S0218339003000907 · Zbl 1041.92044 · doi:10.1142/S0218339003000907
[4] DOI: 10.1080/0003681031000094618 · Zbl 1039.34073 · doi:10.1080/0003681031000094618
[5] DOI: 10.1016/S1468-1218(01)00038-4 · Zbl 0998.92042 · doi:10.1016/S1468-1218(01)00038-4
[6] Bainov D, Impulsive Differential Equations: Periodic Solutions and Applications 66 (1993) · Zbl 0815.34001
[7] Lakshmikantham V, Theory of Impulsive Differential Equations (1989)
[8] DOI: 10.1016/j.amc.2004.09.053 · Zbl 1074.92042 · doi:10.1016/j.amc.2004.09.053
[9] DOI: 10.1016/j.chaos.2003.12.060 · Zbl 1058.92047 · doi:10.1016/j.chaos.2003.12.060
[10] DOI: 10.1142/S0218127405012338 · Zbl 1080.34026 · doi:10.1142/S0218127405012338
[11] DOI: 10.1016/j.chaos.2005.09.059 · Zbl 1145.34029 · doi:10.1016/j.chaos.2005.09.059
[12] DOI: 10.1142/S1793524508000151 · Zbl 1155.92356 · doi:10.1142/S1793524508000151
[13] DOI: 10.1016/j.amc.2007.07.083 · Zbl 1131.92056 · doi:10.1016/j.amc.2007.07.083
[14] DOI: 10.1016/j.jtbi.2006.05.002 · doi:10.1016/j.jtbi.2006.05.002
[15] DOI: 10.1016/j.apm.2007.10.020 · Zbl 1167.34372 · doi:10.1016/j.apm.2007.10.020
[16] DOI: 10.1016/j.tpb.2007.12.001 · Zbl 1208.92093 · doi:10.1016/j.tpb.2007.12.001
[17] DOI: 10.1016/j.mbs.2008.06.008 · Zbl 1156.92046 · doi:10.1016/j.mbs.2008.06.008
[18] DOI: 10.1142/S1793524508000163 · Zbl 1155.92355 · doi:10.1142/S1793524508000163
[19] DOI: 10.1016/j.matcom.2008.02.007 · Zbl 1151.92030 · doi:10.1016/j.matcom.2008.02.007
[20] Gao SJ, Chaos Solitons Fractals
[21] DOI: 10.1142/S1793524508000151 · Zbl 1155.92356 · doi:10.1142/S1793524508000151
[22] DOI: 10.1142/S1793524508000102 · Zbl 1166.92039 · doi:10.1142/S1793524508000102
[23] DOI: 10.1142/S1793524508000072 · Zbl 1155.92045 · doi:10.1142/S1793524508000072
[24] DOI: 10.1016/j.matcom.2008.11.015 · Zbl 1185.34123 · doi:10.1016/j.matcom.2008.11.015
[25] DOI: 10.1007/s002850100121 · Zbl 0990.92033 · doi:10.1007/s002850100121
[26] DOI: 10.1142/S1793524508000266 · Zbl 1173.34043 · doi:10.1142/S1793524508000266
[27] DOI: 10.1016/S0025-5564(00)00068-7 · Zbl 1028.34049 · doi:10.1016/S0025-5564(00)00068-7
[28] DOI: 10.1016/0025-5564(90)90019-U · Zbl 0719.92017 · doi:10.1016/0025-5564(90)90019-U
[29] DOI: 10.1142/S0218127403007011 · Zbl 1063.37586 · doi:10.1142/S0218127403007011
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.