Average decayed dynamics of one-step transformation process with randomly varying return transition rate

The problem of stochastic averaging of the decayed dynamics of the output state population of a one-step transformation process with constant deterministic forward transition rate and randomly varying return transition rate is solved in approximation where random variation is modeled as a dichotomous stochastic process. The form of the obtained solution represented as a product between bimodal sigmoid rise of average population and its unimodal exponential decay is shown to largely be dependent on the stochastic frequency and amplitude parameters. For example, at high stochastic frequency, the behavior of population is reduced to that of a decayed one-step deterministic system. However, for resonance stochastic amplitude at low stochastic frequency, such behavior coincides with that of three-exponential rise-decay kinetics typical rather of a three-step deterministic slowly decaying process. Thus, there is an equivalence between using a more complex deterministic kinetic model and a less complex stochastic kinetic model for describing the decayed dynamics of different irreversible systems.