Noise-Induced Collective Memory in Schooling Fish
Alyssa Chan, Eva Kanso

TL;DR
This paper reveals that collective memory in schooling fish emerges from a noisy bifurcation process, rather than structural bistability, providing new insights into phase transitions in collective animal behavior.
Contribution
It uncovers the mechanism behind collective memory in fish schooling models as a noisy bifurcation, advancing understanding of collective phase transitions.
Findings
Collective memory arises from a noisy transcritical bifurcation.
The transition from milling to schooling is driven by noise-induced bifurcation.
A phenomenological model captures key group dynamics features.
Abstract
Schooling fish often self-organize into a variety of collective patterns, from polarized schooling to rotational milling. Mathematical models support the emergence of these large-scale patterns from local decentralized interactions, in the absence of individual memory and group leadership. In a popular model where individual fish interact locally following rules of avoidance, alignment, and attraction, the group exhibits collective memory: changes in individual behavior lead to emergent patterns that depend on the group's past configurations. However, the mechanisms driving this collective memory remain obscure. Here, we combine numerical simulations with tools from bifurcation theory to uncover that the transition from milling to schooling in this model is driven by a noisy transcritical bifurcation where the two collective states intersect and exchange stability. We further show that…
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