Mathematical Models for Fish Schooling

TL;DR

This paper reviews mathematical models of fish schooling using stochastic differential equations, considering free space, obstacles, and food resources, and provides an example for the case with obstacles and food.

Contribution

It introduces and compares stochastic models for fish schooling in various environments, including obstacles and food sources, with a specific example for the latter case.

Findings

Models effectively simulate fish schooling behavior.

Inclusion of obstacles and food resources enhances model realism.

An example model demonstrates application in complex environments.

Abstract

This note reviews our mathematical models for fish schooling, considered in free space, and in space with obstacle and food resource. These models are performed by stochastic differential equations or stochastic partial differential equations. We then present an example for the model in the last case.