QUANTITATIVE INVESTIGATIONS FOR ODE MODEL DESCRIBING FISH SCHOOLING

Abstract

This paper is devoted to investigating quantitatively the ODE model for fish schooling which was introduced in the paper [15]. First, we will study how each parameter in the model equations contributes to the geometrical structure of the school created by fish such as school diameter, connectedness, graph, etc. Second, we will concentrate on studying effects of the noise imposed to the model equations. In particular, it will be shown that, if the noise’s magnitude is larger than a certain threshold, then fish can no longer form a school.