Persistence and extinction of nonlocal dispersal evolution equations in moving habitats

Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Patrick De Leenheer, Wenxian Shen, Aijun ZhangAbstractThis paper is devoted to the study of persistence and extinction of a species modeled by nonlocal dispersal evolution equations in moving habitats with moving speed c. It is shown that the species becomes extinct if the moving speed c is larger than the so called spreading speed c∗, where c∗ is determined by the maximum linearized growth rate function. If the moving speed c is smaller than c∗, it is shown that the persistence of the species depends on the patch size of the habitat, namely, the species persists if the patch size is greater than some number L∗ and in this case, there is a traveling wave solution with speed c, and it becomes extinct if the patch size is smaller than L∗.

Source: Nonlinear Analysis: Real World Applications - February 9, 2020 Category: Research Source Type: research