  Studies of transient dynamics captures the time history of any dramatic
changes in the dynamics of a system. The transient dynamics is investigated
here in a classic ecological model of a bistable tri-trophic food chain. All
the species in the food chain either coexist or undergoes a partial extinction
with the loss of predator after a transient time that depends upon the initial
density of species populations. The distribution of transient time of
extinction of the predator in response to initial states shows interesting
pattern of inhomogeneity and anisotropy in the basin of predator-fee state.
Precisely, the distribution shows a multimodal character when the initial
points are near the basin boundary, and unimodal at locations far from the
border. The distribution is also anisotropic in the sense that the number of
modes depends on the direction from the basin location. We define two new
metrics, viz., homogeneity index and local isotropic index to characterize the
distinctive features of the distribution. The inhomogeneity of distribution
reduces significantly with resource enrichment, however, a similar change in
anisotropy is relatively low. We try to explain the origin of such multimodal
distributions from the dynamical system perspectives and present its ecological
implications.
