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Mathematical modelling of the electric sense of fish: the role of multi-frequency measurements and movement

by H. Ammari and T. Boulier and J. Garnier and H. Wang

(Report number 2017-11)

Abstract
Understanding active electrolocation in weakly electric fish remains a challenging issue. In this article we propose a mathematical formulation of this problem, in terms of partial differential equations. This allows us to detail two algorithms: one for localizing a target using the multifrequency aspect of the signal, and another one for identifying the shape of this target. Shape recognition is designed in a machine learning point of view, and take advantage of both the multi-frequency setup and the movement of the fish around its prey. Numerical simulations are shown for the computation of the electric field emitted and sensed by the fish; they are then used as an input for the two algorithms.

Keywords: electric fish, electrolocation, shape recognition, learning approach

@Techreport{ABGW17_707,
  author = {H. Ammari and T. Boulier and J. Garnier and H. Wang},
  title = {Mathematical modelling of the electric sense of fish: the role of multi-frequency measurements and movement
},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-11},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-11.pdf },
  year = {2017}
}

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