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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