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How do the spatial structure and time delay affect the persistence of a polluted species. (English) Zbl 1039.34073

The author analyzes toxicant-population models with discrete diffusion or time delay. It is shown that there exists a threshold for each system such that below the threshold the population is uniformly persistent, and above the threshold the population goes to extinction. It is shown that dispersal allows a large threshold, that is, dispersal can increase the endurance effectiveness of the population subject to a toxicant, and time delay has no effect on the threshold result.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics (general)
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[1] DOI: 10.1111/j.1523-1739.1991.tb00384.x
[2] Diamond J., Conservation for the Twenty-first Century (1989)
[3] DOI: 10.1016/0304-3800(83)90019-4
[4] DOI: 10.1007/BF00275908 · Zbl 0548.92019
[5] Hallam T.G., J. Math. Biol., IA pp 327– (1986) · Zbl 0606.92022
[6] Zhien Ma, Bull. Math. Biol. 51 pp 311– (1989) · Zbl 0676.92010
[7] DOI: 10.1016/0025-5564(90)90103-6 · Zbl 0714.92027
[8] DOI: 10.1007/BF00168006 · Zbl 0745.92028
[9] DOI: 10.1006/jmaa.1997.5387 · Zbl 0905.92030
[10] Yucun C., Chinese Wildlife pp 3– (1994)
[11] Xiao Y.N., System Science and Mathematical Science 12 pp 344– (1999)
[12] Beretta E., Bull. Math. Biol. 49 pp 431– (1987)
[13] Hale J.K., Theory of Functional Differential Equations (1977) · Zbl 0352.34001
[14] Environment Pollution and Plant (1978)
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