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Abstract
A discrete-time, two-stage host population model in which adults may consume their offspring is proposed and analysed. It is shown that the population is stabilized at the unique interior equilibrium if the basic reproductive number of the population is larger than one and the population is not cannibalistic. If the mechanism of cannibalism is incorporated, then the model undergoes a discrete Hopf (Neimark–Sacker) bifurcation when the interior equilibrium loses its stability. We also study a system of host–parasitoid interaction based on the two-stage host population model. Numerical simulations suggest that the introduction of parasitoid may stabilize the system when the host population is oscillating in the absence of parasitoid.
Acknowledgements
We thank one of the referees for providing suggestions and references on improving the paper. S. Jang acknowledges the financial support from Mathematics Research Promotion Center, National Science Council of Taiwan, for her winter 2009–2010 visit to Taiwan during which the research was completed. J. Yu was supported by National Science Council of Taiwan under Grant Nos. NSC 98-2115-M-126-001.