Robust moth olfactory search algorithm based on dispersion of pheromone puffs

Female moths attract male moths by emitting to the atmosphere a series of pheromone filaments propagating downwind. The filaments appear to be aggregated into clusters (patches) while moving. In order to find the female moth, the male moth senses the concentration of the pheromone (e.g. odour) dispersed within the patches. Using the odour as a cue, the male moth may reach the vicinity of the female moth. The spatial and temporal variations of the odour advected by turbulence are random. This work addresses the problem of a male moth searching a female moth by tracing the randomly varying odour. We suggest an algorithm of searching the odour source. The algorithm uses a single instantaneous parameter that a navigator can measure: the time the moth crossed the odour patch during the last search. We describe mathematically a turbulent meandering patchy plume and the odour inside the plume. Using the proposed navigation algorithm, we simulate the path of the male moth searching the female moth. Numerical simulations illustrate a strong similarity between the simulated paths and those reported in the literature. Using the suggested algorithm, we estimate the probability of a male moth to reach close to a female moth. This simulated probability is in satisfactory agreement with that observed in reported results of experiments.