We propose a numerical algorithm for calculation of quantized directed motion of a stochastic systemof interacting particles induced by periodic changes of control parameters on the graph of microstates.As a main application, we consider models of catenane molecular motors, which demonstratedthe possibility of a similar control of directed motion of molecular components. We showthat our algorithm allows one to calculate the motion of a system in the space of its microstateseven when the considered phase space is combinatorially large (∼1 × 106 microscopic states). Severalgeneral observations are made about the structure of the phase diagram of the systems studied,which may be used for rational design and efficient control of new generations of molecular motors.
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