A variety of spatial patterns are formed chemotactically by the bacteria
Escherichia coli and
Salmonella typhimurium. We focus in this paper on patterns formed by
E. coli and
S. typhimurium in liquid medium experiments. The dynamics of the bacteria, nutrient and chemoattractant are modeled mathematically and give
rise to a nonlinear partial differential equation system.
We present a simple and intuitively revealing analysis of the patterns generated by our model. Patterns arise from disturbances
to a spatially uniform solution state. A linear analysis gives rise to a second order ordinary differential equation for the
amplitude of each mode present in the initial disturbance. An exact solution to this equation can be obtained, but a more
intuitive understanding of the solutions can be obtained by considering the rate of growth of individual modes over small
time intervals.
Key words: Chemotaxis - Partial differential equations - Bacteria - Mathematical Modeling - Pattern formation
Received: 10 March 1998 / Revised version: 7 June 1998