A study of a three species food chain

We study the dynamics of a food web consisting of three species of fish, extending previously obtained results. We have used two different approaches: looking for the asymptotic states of the system, resulting from numerical integration of the equations; and the application of the embedding procedure, to extract the relevant dynamical exponents, from a time series for only one scalar variable. The two approaches are complementary, the first helps emphasize geometrical aspects. In the second, orbit stability is exhibited and, via the possibility of the method of Ott et al. (Phys. Rev. Lett. 64 (1990) 1196) for chaos control, this opens issues to be studied in the future.