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

TL;DR

This paper develops a mathematical model for weakly electric fish's active electrolocation, utilizing multi-frequency measurements and movement to improve target localization and shape identification through algorithms and simulations.

Contribution

It introduces a PDE-based mathematical formulation and two algorithms that leverage multi-frequency data and fish movement for electrolocation tasks.

Findings

Algorithms successfully localize targets using multi-frequency signals.

Shape recognition benefits from fish movement and multi-frequency data.

Numerical simulations validate the proposed methods.

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 multi-frequency aspect of the signal, and antoher 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.