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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.

34D05Asymptotic stability of ODE
Full Text: DOI
[1] Brown, W. K.: Burwash uplands caribou herd: distribution and movement studies. Report for foothills pipelines (Yukon) ltd. (1981)
[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
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[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. Canadian wildlife service publication series (Sept. 28, 1983)
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