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

Structural sensitivity of chaotic dynamics in Hastings-Powell's model