Global dynamics of population-toxicant models with nonlocal dispersals

Abstract In the article, we first investigate a population-toxicant model with nonlocal dispersal. Compared to the local dispersal (random dispersal), nonlocal dispersal brings some difficulties. One of the difficulties is that principal eigenvalue might not exist. Another difficulty is that the solution orbits lose their compactness. Motivated by previous studies, we overcome these difficulties and establish the global dynamics by spectral analysis, the methods of lower and upper solutions, and the theory of abstract monotone dynamical system. Then, we generalize these results to more general case that the dispersal strategies are mixture of local and nonlocal dispersals. Finally, we point out that we have successfully expanded the upper bound of the critical indicator given in the study by Zhou and Huang without advection terms.