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**Mathematical models of population interactions with dispersal. II: Differential survival in a change of habitat.**
*(English)*
Zbl 0588.92020

[For part I see SIAM J. Appl. Math. 32, 631-648 (1977; Zbl 0362.92006).] - The paper considers a model of dispersing populations in the form of a system of nonlinear ordinary differential equations. Dispersal pressure is density dependent and a parameter measures the barrier strength. The model also incorporates a transition probability to allow for a risk in changing habitats.

For the two-dimensional case, the region in parameter space for existence of a stable equilibrium solution is exactly determined, bounded in part by a branch of a hyperbola. For the n-dimensional case, similar, but less complete results are obtained.

For the two-dimensional case, the region in parameter space for existence of a stable equilibrium solution is exactly determined, bounded in part by a branch of a hyperbola. For the n-dimensional case, similar, but less complete results are obtained.

### Keywords:

global asymptotic stability; dispersing populations; nonlinear ordinary differential equations; Dispersal pressure; barrier strength; transition probability; risk in changing habitats; existence of a stable equilibrium solution### Citations:

Zbl 0362.92006
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\textit{H. I. Freedman} et al., J. Math. Anal. Appl. 115, 140--154 (1986; Zbl 0588.92020)

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### References:

[1] | Brown, W.K, Burwash uplands caribou herd: distribution and movement studies, () |

[2] | Chewning, W.C, Migratory effects in predation prey systems, Math biosci., 23, 253-262, (1975) · Zbl 0301.92010 |

[3] | Freedman, H.I; Waltman, P, Mathematical models of population interaction with dispersal I: stability of two habitats with and without a predator, SIAM J. appl. math, 32, 631-648, (1977) · Zbl 0362.92006 |

[4] | {\scD. A. Gauthier}, “Mountain caribou movements in relation to the proposed gas pipeline of Foothills Pipelines (South Yukon) Ltd, Kluane Lake Region,” Yukon Wildlife branch report 1979, Whitehorse, Yukon. |

[5] | Gauthier, D.A; Brown, W.K; Theberge, J.B, Movement and distribution of the burwash caribou herd relative to the proposed alaska highway gas pipeline, () |

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[7] | Holt, R.D, Population dynamics in two patch environments; some anomalous consequences of optional habitat selection, Theor. pop. biol., 28, 181-208, (1985) · Zbl 0584.92022 |

[8] | Levin, S.A, Dispersion and population interactions, Amer. natur., 108, 207-228, (1974) |

[9] | Levin, S.A, Spatial patterning and the structure of ecological communities, () · Zbl 0338.92017 |

[10] | {\scL. A. Segel and S. A. Levin}, Application of nonlinear stability theory to the study of the effects of diffusion on predator-prey interactions, “Proc. AIP Conference” (Festschuft for Julius Jackson). |

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