Food chain chaos with canard explosion.

The "tea-cup" attractor of a classical prey-predator-superpredator food chain model is studied analytically. Under the assumption that each species has its own time scale, ranging from fast for the prey to intermediate for the predator and to slow for the superpredator, the model is transformed into a singular perturbed system. It is demonstrated that the singular limit of the attractor contains a canard singularity. Singular return maps are constructed for which some subdynamics are shown to be equivalent to chaotic shift maps. Parameter regions in which the described chaotic dynamics exist are explicitly given.

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