Modeling Active Electrolocation in Weakly Electric Fish
In this paper, we provide a mathematical model for the electrolocation in weakly electric fishes. We first investigate the forward complex conductivity problem 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 noniterative location search algorithm using multifrequency measurements. We present numerical experiments to illustrate the performance and the stability of the proposed multifrequency location search algorithm. Finally, in the case of disk and ellipse-shaped targets, we provide a method for reconstructing separately the conductivity, the permittivity, and the size of the targets from multifrequency measurements.
weakly electric fish approximate boundary conditions location search algorithm multifrequency music algorithm