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Abstract: We study the dynamical complexity of five non-linear deterministic predator–prey model systems. These simple systems were selected to represent a diversity of trophic structures and ecological interactions in the real world while still preserving reasonable tractability. We find that these systems can dramatically change attractor types, and the switching among different attractors is dependent on system parameters. While dynamical complexity depends on the nature (e.g., inter-specific competition versus predation) and degree (e.g., number of interacting components) of trophic structure present in the system, these systems all evolve principally on intrinsically noisy limit cycles. Our results support the common observation of cycling and rare observation of chaos in natural populations. Our study also allows us to speculate on the functional role of specialist versus generalist predators in food web modeling. [Copyright &y& Elsevier]