Abstract. The biological process of cooperative interaction with equilibrium state is described as a model of binary statistical experiments with the Wright–Fisher normalization, which describes the concentration of a certain characteristic. Such a mathematical model is supposed to have a property of persistent regression, which means that all current elementary transitions depend on the mean concentration of the said characteristics in the previous state. Equilibrium state of the model is expressed in the terms of the regression function given by a cubic parabola with three real roots. We construct the stochastic approximation of the model by autoregressive process with normal disturbances. Such an approach was developed for effective and calculable mathematical description of dynamic concentration for experiment planning, parameter evaluation, and verification of hypotheses of the mechanisms of action.

Keywords: binary statistical experiment, persistent regression, Wright–Fisher normalization, equilibrium state, normal autoregression.