  Predicting the evolution of expanding population is critical to control
biological threats such as invasive species and virus explosion. In this paper,
we consider a two species chemotaxis system of parabolic-parabolic-elliptic
type with Lotka-Volterra type competition terms and a free boundary. Such a
model with a free boundary describes the spreading of new or invasive species
subject to the influence of some chemical substances in an environment with a
free boundary representing the spreading front. We first find conditions on the
parameters which guarantee the global existence and boundedness of classical
solutions with nonnegative initial functions. Next, we investigate
vanishing-spreading dichotomy scenarios for positive solutions. It is shown
that the vanishing-spreading dichotomy in the generalized sense always occurs;
that the vanishing spreading dichotomy in the strong sense occurs when the
competition between two species is weak-weak competition; and that the
vanishing spreading dichotomy in the weak sense occurs when the competition
between two species is weak-strong competition.
