Mathematical model of schooling behavior of fish observed in laboratory water tank experiment
2002
"Mori, T. (Niigata Univ. (Japan)) | Okaguchi, M. | Morii, T. "
Schooling behavior of fish is observed in a shallow water tank. Bitterling about 4-6 cm in body length are employed in the laboratory experiments. The schooling behavior of fish observed is compared with results of a numerical simulation based on a Newtonian dynamics model. An individual fish that forms the fish school is assumed as a mass particle in the Newtonian dynamic model. Interactions acting among the mass particles are introduced into a set of nonlinear differential equations of motion to take external forces that cause the schooling behavior of fish into account. Effects of environmental field within the water tank are also considered in constructing the set of differential equations. A part of laboratory observations of the schooling behavior is well explained by the Newtonian dynamics model. But a practical difficulty to determine a set of model parameters that are required in the numerical calculations is noticed. As well it is shown that the Newtonian dynamics model cannot describe the behavior of individual fish induced by a biological but unforeseen impact. A small recommendation to couple a hydraulic engineering model with the mathematical model of schooling behavior of fish is given lastly.
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