Modeling active electrolocation in weakly electric fish

Details Modeling active electrolocation in weakly electric fish Modeling active electrolocation in weakly electric fish

2012-03-05

arxiv.org/abs/1203.0938v1

Mathematics

Analysis of PDEs

Scientific paper

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 approx- imate 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 search algorithm using multi-frequency measurements. We present numerical experi- ments to illustrate the performance and the stability of the proposed multi-frequency location search algorithm. Finally, in the case of disk- and ellipse-shaped targets, we provide a method to reconstruct separately the conductivity, the permittivity, and the size of the targets from multi-frequency measurements.

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