  The possibility of using non-deterministic circuit components has been
gaining significant attention in recent years. The modeling and simulation of
their circuits require novel approaches, as now the state of a circuit at an
arbitrary moment in time cannot be precisely predicted. Generally, these
circuits should be described in terms of probabilities, the circuit variables
should be calculated on average, and correlation functions should be used to
explore interrelations among the variables. In this paper, we use, for the
first time, a master equation to analyze the networks composed of probabilistic
binary memristors. Analytical solutions of the master equation for the case of
identical memristors connected in-series and in-parallel are found. Our
analytical results are supplemented by results of numerical simulations that
extend our findings beyond the case of identical memristors. The approach
proposed in this paper facilitates the development of probabilistic/stochastic
electronic circuits and advance their real-world applications.
