Abstract
A biased one-dimensional random walk model is proposed. This model adopts biased rules that include the features of bacterial chemo-taxis. In this model, a model cell moves along a discretized number line sensing whether it has approached or receded from the origin where a chemical attractant exists. A steady probability distribution function of the cell's existence is analytically obtained and it is confirmed by numerical simulations. The biased rules introduce advection effect into random diffusive motion: the probability distribution indicates model cells' accumulation around the origin, which corresponds to the spatial migration of bacterial cells around a chemical attractant.
