The effect of reversals for a stochastic source-seeking process inspired by bacterial chemotaxis

Many species of bacteria are motile, but they use different random strategies to determine where to swim in response to chemical gradients. We extend past work describing a chemotactic E. coli cell as an ergodic, stochastic hybrid system to model a variety of different strategies. We quantify differences in asymptotic performance and show that the processes described by our models converge to stationary distributions that are proportional to various powers of the distribution of chemicals in the environment. Our main goal is to understand the implications of the differences between E. coli´s chemotaxis strategy and the more complicated strategy of the marine bacterium Vibrio alginolyticus, which, unlike E. coli, can swim both forward and backward. We argue that Vibrio´s ability to reverse allows it to accumulate more tightly around nutrient sources, and we quantify the effects that reversals have on the stationary distribution of various processes. Our results provide intuition for designing minimalistic multi-agent robotic systems that are better suited for source-seeking tasks in particular environments.