One of the major operators of Bacterial Foraging Optimization Algorithm (BFOA) is the reproduction phenomenon of virtual bacteria each of which models one trial solution of the optimization problem. During reproduction, the least healthier bacteria (with a lower accumulated value of the objective function in one chemotactic lifetime) die and the other healthier bacteria each split into two, which then starts exploring the search place from the same location. Thus the population size is maintained constant in BFOA. In this paper we try to model the reproduction dynamics and then analyzed the stability of the reproductive system very near to equilibrium. We also find the relative positions of two bacteria for which a stable reproduction event can take place in a one dimensional fitness landscape
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