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

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
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\textit{J. Cui} et al., Comput. Math. Appl. 39, No. 1--2, 91--102 (2000; Zbl 0968.92018)

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### 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 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, () |

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