A STUDY OF A 3 SPECIES FOOD-CHAIN

We study the dynamics of a food web consisting of three species of fis h, extending previously obtained results. We have used two different a pproaches: looking for the asymptotic states of the system, resulting from numerical integration of the equations; and the application of th e embedding procedure, to extract the relevant dynamical exponents, fr om a time series for only one scalar variable. The two approaches are complementary, the first helps emphasize geometrical aspects. In the s econd, orbit stability is exhibited and, via the possibility of the me thod of Ott et al. (Phys. Rev. Lett. 64 (1990) 1196) for chaos control , this opens issues to be studied in the future. (C) 1998 Elsevier Sci ence B.V. All rights reserved.