  The current series of research papers is to investigate the asymptotic
dynamics in logistic type chemotaxis models in one space dimension with a free
boundary or an unbounded boundary. Such a model with a free boundary describes
the spreading of a new or invasive species subject to the influence of some
chemical substances in an environment with a free boundary representing the
spreading front. In this first part of the series, we investigate the dynamical
behaviors of logistic type chemotaxis models on the half line $\mathbb{R}^+$,
which are formally corresponding limit systems of the free boundary problems.
In the second of the series, we will establish the spreading-vanishing
dichotomy in chemoattraction-repulsion systems with a free boundary as well as
with double free boundaries.
