  The classical Hastings-Powell model is well known to exhibit chaotic dynamics
in a three-species food chain. Chaotic dynamics appear through period-doubling
bifurcation of stable coexistence limit cycle around an unstable interior
equilibrium point. A specific choice of parameter value leads to a situation
where the chaotic attractor disappears through a collision with an unstable
limit cycle. As a result, the top predator goes to extinction. Here we explore
the structural sensitivity of this phenomenon by replacing the Holling type II
functional responses with Ivlev functional responses. Here we prove the
existence of two Hopf-bifurcation thresholds and numerically detect the
existence of an unstable limit cycle. The model with Ivlev functional responses
does not indicate any possibility of extinction of the top predator. Further,
the choice of functional responses depicts a significantly different picture of
the coexistence of the three species involved with the model.
