  In this paper, we are concerned with a two-species competitive model with
diffusive terms on a periodically evolving domain and study the impact of the
spatial periodic evolution on the dynamics of the model. The Lagrangian
transformation approach is adopted to convert the model from a changing domain
to a fixed one with the assumption that the evolution of habitat is uniform and
isotropic. The ecological reproduction indexes of the linearized model are
given as thresholds to reveal the dynamic behaviour of the competitive model by
discussing the relations between the initial boundary value problem and its
corresponding periodic problem. Our theoretical results show that a lager
evolving rate benefits the persistence of competitive populations for both
sides in the long run. Numerical experiments illustrate that two competitive
species, one of which survive and the other vanish on a fixed domain, both
survive on a domain with a large evolving rate and both vanish on a domain with
a small evolving rate.
