A new mathematical model for the motion of a fish school with many individuals is proposed. The basic assumption for model building is that the behavior of fish school can be decomposed into two components. One is the motion of a fictitious individual called the gravity center of the school. The other is the motion of four individuals which are located at the boundary of the school. The validity of the model is examined from a simulation result.
To overcome the difficulty in obtaining observational data offish behaviour, an aggregated model is presentedfor studying the behaviour ofa fish school with many individuals. In this model, the motion ofafish school is described by the motions of the centre of gravity of the school and four representative individuals which are located at the boundary of the school. In this study, the behaviour of a fish school with 20 individuals swimming in a water tank is investigated by using this model. A simulation is carried out for the same boundary condition as the water tank experiment. Consequently, the difference ofthe behaviour between the centre ofgravity and the four individuals as well as the relationship between the school speed and school size is analysed by comparing the simulation result with the observation data.
An observation data is obtained for an irregular swimming trajectory of fish school in a water tank experiment. The motion of fish school under the influence of disturbances is described by a mathematical model with random variables which are modelled as independent, white and Gaussian quantities. A simulation is carried out corresponding to the observation data, and quantitative similarity is obtained in an average sense.
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