Abstract
This paper is concerned with a prey-predator model with sign-changing intrinsic growth rate in heterogeneous time-periodic environment, where the prey species lives in the whole space but the predator species lives in a region enclosed by a free boundary. It is shown that the results for the case of the non-periodic environment remain true in time-periodic environment. In fact, we first establish a similar spreading-vanishing dichotomy, which implies that if the predator species could spread successfully, then the two species will coexist, and this is certainly for the situation that the predation is relatively weak. Furthermore, some criteria are also obtained for spreading and vanishing. At last, some rough estimates of the asymptotic spreading speed are given if spreading occurs.
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