In this paper, we provide a mathematical model for the electrolocation inweakly electric fishes. We first investigate the forward complex conductivityproblem and derive the approximate boundary conditions on the skin of the fish.Then we provide a dipole approximation for small targets away from the fish.Based on this approximation, we obtain a non-iterative location searchalgorithm using multi-frequency measurements. We present numerical experimentsto illustrate the performance and the stability of the proposed multi-frequencylocation search algorithm. Finally, in the case of disk- and ellipse-shapedtargets, we provide a method to reconstruct separately the conductivity, thepermittivity, and the size of the targets from multi-frequency measurements.
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