Abstract
This paper deals with mathematical modeling of fish behavior in a water tank. The model presented in our earlier papers describes the behavior of each individual in a school. Then, it is applicable to the case of small school.In this paper, an aggregation model is presented on the basis of the following assumption : The schooling behavior of fish can be decomposed into two components. One is the motion of a representative of the school. The other is the variation of the school size. Since the model for the representative was presented previously, the present study is directed toward the model for the school size. An autoregressive model is presented for this purpose. The model order is determined by minimizing the AIC. The unknown parameters are estimated by applying the least squares algorithm. The validity of the autoregressive model is examined by a residual whiteness test and a simulation study.
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