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.
- Discrete hopf bifurcation
- Uniform persistence