  The objective of this paper is to study the dynamical behaviour
systematically of an ecological system with Beddington-DeAngelis functional
response which avoids the criticism occurred in the case of ratio-dependent
functional response at the low population density of both the species. The
essential mathematical features of the present model have been analyzed
thoroughly in terms of the local and the global stability and the bifurcations
arising in some selected situations as well. The threshold values for some
parameters indicating the feasibility and the stability conditions of some
equilibria are also determined. We show that the dynamics outcome of the
interaction among the species are much sensitive to the system parameters and
initial population volume. The ranges of the significant parameters under which
the system admits a Hopf bifurcation are investigated. The explicit formulae
for determining the stability, direction and other properties of bifurcating
periodic solutions are also derived with the use of both the normal form and
the central manifold theory (cf. Carr \cite{Carr}). Numerical illustrations are
performed finally in order to validate the applicability of the model under
consideration.
