# Modeling Adaptive Tracking of Predictable Stimuli in Electric Fish

arXiv: https://arxiv.org/abs/2509.15344 · HTML: https://mlsanity.com/paper/2509.15344/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2025.

## Built on by (most cited first, 1 of 1)

- [Active Sensing Subserves Task-Level Control](https://mlsanity.com/paper/2605.22988/) (2026)

## Abstract (arXiv)

The weakly electric fish Eigenmannia virescens naturally swims back and forth to stay within a moving refuge, tracking its motion using visual and electrosensory feedback. Previous experiments show that when the refuge oscillates as a low-frequency sinusoid (below about 0.5 Hz), the tracking is nearly perfect, but phase lag increases and gain decreases at higher frequencies. Here, we model this nonlinear behavior as an adaptive internal model principle (IMP) system. Specifically, an adaptive state estimator identifies the a priori unknown frequency, and feeds this parameter estimate into a closed-loop IMP-based system built around a lightly damped harmonic oscillator. We prove that the closed-loop tracking error of the IMP-based system, where the online adaptive frequency estimate is used as a surrogate for the unknown frequency, converges exponentially to that of an ideal control system with perfect information about the stimulus. Simulations further show that our model reproduces the fish refuge tracking Bode plot across a wide frequency range. These results establish the theoretical validity of combining the IMP with an adaptive identification process and provide a basic framework in adaptive sensorimotor control.