Existence of forced waves and gap formations for a Lotka-Volterra competition system with nonlocal dispersal in a time periodic shift habitat

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This paper is devoted to the study of a class of time periodic Lotka-Volterra competition system with nonlocal dispersal and shifting habitats. By using some known results of the periodic KPP model and employing the iterative techniques, we prove that there exist two positive numbers $c_{0}(d_{1})$ and $c_{0}(d_{2})$ such that the system admits a forced wave provided that the forcing speed $c\in(-c_{0}(d_{2}),c_{0}(d_{1}))$. In addition, based on the theoretical results, we show that the gap formations exist for $c>c_{0}(d_{1})$ and $c<-c_{0}(d_{2})$.