Chaos and fractals in fish school motion

The once abstract notions of fractal patterns and processes now appear natu rally and inevitably in various chaotic dynamical systems. The examples ran ge from Brownian motion [1-5] to the dynamics of social relations [6]. In t his paper, after introducing a certain hybrid mathematical model of the pla nkton-fish school interplay, we study the fractal properties of the model f ish school walks. We show that the complex planktivorous fish school motion is dependent on the fish predation rate. A decrease in the rate is followe d by a transition from low-persistent to high-persistent fish school walks, i.e., from a motion with frequent to a motion with few changes of directio n. The low-persistent motion shows fractal properties for all time scales, whereas the high-persistent motion has pronounced multifractal properties F or large-scale displacements. (C) 2000 Elsevier Science Ltd. All rights res erved.