Spreading speeds and forced waves of a three species competition system with nonlocal dispersal in shifting habitats

This paper is concerned with propagation phenomenon of a three species competition system with nonlocal dispersal in shifting habitats. We first give the existence of two types of forced wave connecting origin to only one species state and semi-co-existence state in supercritical and critical cases. Then, we get the existence of forced waves connecting origin to coexistence state at any speed. In particular, we establish the spreading property of the associated Cauchy problem depending on the range of the shifting speed which is identified respectively by (i) extinction of three species; (ii) only one species surviving; (iii) two species coexisting; (iv) persistence of three species.