This work studies two mathematical models for describing the motion of phototaxis, i.e., bacteria that move towards light. Based on experimental observations, we conjecture that the motion of the colony towards light depends on certain group dynamics. This group dynamics is assumed to be encoded as an individual property of each bacterium, which we refer to as 'excitation'. The excitation of each individual bacterium changes 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.