The effect of dispersal on population growth with stage-structure. (English) Zbl 0968.92018

Cui, Jingan; Chen, Lansun; Wang, Wendi

Comput. Math. Appl. 39, No. 1-2, 91-102 (2000).

Summary: Declines in species richness or population are primarily attributed to habitat destruction and fragmentation. Can we avoid the local extinction of species with stage-structure in some patches by building some corridors between the patches and controlling the dispersal rates? A conservation strategy is put forward by introducing and analyzing the asymptotic behavior of some autonomous and time-varying population models. Biological implications of these results are discussed briefly.

MSC:

92D25	Population dynamics (general)
34D23	Global stability of solutions to ordinary differential equations
92D40	Ecology
37N25	Dynamical systems in biology
34D05	Asymptotic properties of solutions to ordinary differential equations
34C25	Periodic solutions to ordinary differential equations

Keywords:

dispersal

References:

[1]	Allen, L. J.S., Persistence and extinction in single species reaction-dispersal models, Bull. Math. Biol., 45, 209-227 (1983) · Zbl 0543.92020
[2]	Freedman, H. I.; Rai, B.; Waltman, P., Mathematical model of population interactions with dispersal II. Differential survival in a change of habitat, J. Math. Anal. Appl., 115, 140-154 (1986) · Zbl 0588.92020
[3]	Hastings, A., Dynamics of a single species in a spatially varying environment: The stabilizing role of high dispersal rates, J. Math. Biology, 16, 49-55 (1982) · Zbl 0496.92010
[4]	Holt, R. D., Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution, Theoret. Population Bio., 28, 181-208 (1985) · Zbl 0584.92022
[5]	Takeuchi, Y., Cooperative system theory and global stability of dispersal models, Acta Appl. Math., 14, 49-57 (1989) · Zbl 0665.92017
[6]	Vance, R. R., The effect of dispersal on population stability in one-species, discrete space population growth models, The American Naturalist, 123, 230-254 (1984)
[7]	Cui, J.; Chen, L., The effect of dispersal on the time varying logistic population growth, Computers Math. Applic., 36, 3, 1-9 (1998) · Zbl 0934.92025
[8]	Mahbuba, R.; Chen, L., On the nonautonomous Lotka-Volterra competition system with dispersal, Differential Equations and Dynamical Systems, 2, 243-253 (1994) · Zbl 0874.34048
[9]	Wang, W.; Chen, L., Global stability of a population dispersal in a two-patch environment, Dynamic Systems and Applications, 6, 207-216 (1997) · Zbl 0892.92026
[10]	Aiello, W. G.; Freedman, H. I., A time-delay model of single-species growth with stage structure, Math. Biosci., 101, 139-153 (1990) · Zbl 0719.92017
[11]	Aiello, W. G.; Freedman, H. I.; Wu, J., Analysis of a model representing stage-structure population growth with state-dependent time delay, SIAM J. Appl. Math., 52, 855-869 (1992) · Zbl 0760.92018
[12]	Wang, W.; Chen, L., A predator-prey system with stage-structure for predator, Computers Math. Applic., 33, 8, 83-91 (1997)
[13]	Bernard, O.; Souissi, S., Qualitative behavior of stage-structure populations: Application to structural validation, J. Math. Biol., 37, 291-308 (1998) · Zbl 0919.92035
[14]	Wang, S.; Qu, Y.; Jing, Z.; Wu, Q., Research on the suitable living environment of the Rana temporaria chensinensis larva, Chinese Journal of Zoology, 32, 1, 38-41 (1997)
[15]	Deng, X.; Deng, Z., Progress in the conservation biology of Chinese sturgeon, Zoological Research, 18, 1, 113-120 (1997)
[16]	Zhou, Y., Analysis on decline of wild alligator sinensis population, Sichuan Journal of Zoology, 16, 3, 137-139 (1997)
[17]	Li, X.; Li, D., Population viability analysis for the crested Ibis (Nipponia nippon), Chinese Biodiversity, 4, 2, 69-77 (1996)
[18]	Hirsch, M. W., The dynamical systems approach to differential equations, Bull. A.M.S., 11, 1-64 (1984) · Zbl 0541.34026
[19]	Lancaster, P.; Tismenetsky, M., The Theory of Matrices (1985), Academic Press · Zbl 0516.15018
[20]	Edelstein-keshet, L., Mathematical Models in Biology (1988), Random House: Random House New York · Zbl 0674.92001
[21]	Smith, H. L., Cooperative systems of differential equation with concave nonlinearities, Nonlinear Analysis, 10, 1037-1052 (1986) · Zbl 0612.34035
[22]	Krasnoselskii, M. A., The operator of translation along trajectories of differential equations, (Translations of Math. Monographs, Volume 19 (1968), Am. Math. Soc: Am. Math. Soc Providence, RI)