Two species nonlocal diffusion systems with free boundaries

<p style='text-indent:20px;'>We study a class of free boundary systems with nonlocal diffusion, which are natural extensions the corresponding problems reaction diffusion systems. As before represents spreading front species, but here population dispersal is described by "nonlocal diffusion" instead "local diffusion". We prove that such problem has unique global solution, and for models Lotka-Volterra type competition or predator-prey growth terms, we show spreading-vanishing dichotomy holds, obtain criteria vanishing; moreover, weak case predation case, can determine long-time asymptotic limit solution when happens. Compared single species model considered recently in [<xref ref-type="bibr" rid="b7">7</xref>], two cases local extensively studied literature, situation this paper involves several new difficulties, overcome use some techniques.</p>