Studies on the Schooling Behavior of Fish—V. Note on the Dynamics of Fish Schooling

Abstract

A dynamical model for fish schooling is presented. The basic equation of motion of individual fish contains mutual attraction or repulsion of fish around its equilibrium position, frictional force due to locomotion, and the swimming force. The concept of an average time lag (“latency”) is introduced to the swimming force. As a result, the speed of school and the dimension of school obey the same dynamical equation correct to the first order of the time lag, and accordingly the corresponding frequency spectra behave in the same manner. The theoretical spectrum shows a minus four power law at large values of frequency. The cross-correlation between the change of the school form and the school speed has a time lag about one second on the positive side from the origin. These theoretical results compare favorably with the experimental results obtained in the previous studies. © 1977, The Japanese Society of Fisheries Science. All rights reserved.