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Abstract. We study the search kinetics of an immobile target by a concentration of randomly moving searchers. The object of the study is to optimize the probability of detection within the constraints of our model. The target is hidden on a onedimensional lattice in the sense that searchers have no a priori information about where it is, and may detect it only upon encounter. The searchers perform random walks in discrete time n = 0, 1, 2, . . . , N , where N is the maximal time the search process is allowed to run. With probability α the searchers step on a nearest-neighbour, and with probability (1 − α) they leave the lattice and stay off until they land back on the lattice at a fixed distance L away from the departure point. The random walk is thus intermittent. We calculate the probability P N that the target remains undetected up to the maximal search time N , and seek to minimize this probability. We find that P N is a non-monotonic function of α, and show that there is an optimal choice α opt (N ) of α well within the intermittent regime, 0 < α opt (N ) < 1, whereby P N can be orders of magnitude smaller compared to the "pure" random walk cases α = 0 and α = 1.

We study the role of potential symmetry in a three-field reaction-diffusion system presenting bistability by means of a two-state theory for stochastic resonance in general asymmetric systems. By analyzing the influence of different parameters in the optimization of the signal-to-noise ratio, we observe that this magnitude always increases with the symmetry of the system's potential, indicating that it is this feature which governs the optimization of the system's response to periodic signals.