The paper describes a discrete time model that describes the dynamics of interaction between two consumers. Within the deterministic analysis, zone of coexistence of at least two equilibria was found. The zones of coexistence of three and more attractors were determined, and the bifurcations were described. The fractal structure of the basins of attraction were shown. The behavior of stochastic version of this model is described. The effect of additive and parametric noise on the system was studied. Using the stochastic sensitivity function, a comparative analysis of the sensitivity for equilibria and cycles was carried out. Based on the method of confidante ellipses, values of the noise intensity at which a transition from one attractor to another is observed. The formation of a new stochastic attractor was obtained.