Stochastic models for phototaxis

This work studies two mathematical models for describing the motion of phototactic bacteria, i.e., bacteria that move toward light. Based on experimental observations, we conjecture that the motion of the colony toward light depends on certain group dynamics. These group dynamics are hypothesized to be coordinated through an individual property of each bacterium, which we refer to as excitation. The excitation of each individual bacterium is assumed to change based on the excitation of the neighboring bacteria. Under these assumptions, we propose a (discrete) cellular automaton model and derive an analogous stochastic model for describing the evolution in time of the location of bacteria, the excitation of individual bacteria, and a surface memory effect. We provide simulation results and discuss in detail the role of the various model parameters in controlling the emerging dynamics.