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Traveling periodic waves in heterogeneous environments. (English) Zbl 0591.92026
Summary: A model for a single species population which propagates in a heterogeneous environment in a one dimensional space is presented. The environment is composed of two kinds of patches with different diffusivities and intrinsic growth rates, which are alternately arranged along the spatial axis.
From the stability analysis of the model, the invasion condition for a new migrating species is obtained in terms of the sizes of patches, diffusivities and growth rates. When the parameters satisfy the invasion condition, the distribution of the population initially localized in a bounded area always evolves into a traveling periodic wave (TPW) with a constant speed.
When the invasion condition is not satisfied, the population fails in invasion tending to extinction. The velocity of TPW is calculated by using a dispersion relation, and the effects of the heterogeneity of the environment on the velocity are discussed.

MSC:
92D40 Ecology
35K99 Parabolic equations and parabolic systems
35Q99 Partial differential equations of mathematical physics and other areas of application
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