Abstract
In this paper, we consider a three-species intraguild predation (IGP) model which includes a predator (IG predator) and its prey (IG prey) that share a common resource, and where the IG prey population is partitioned into juvenile and adult stages. The juvenile IG prey are assumed to have little ability for predation and are able to avoid the IG predators by taking refuge. The maturation age of the IG prey population is reflected by a time delay. Conditions for the existence and local stability of all non-negative equilibria are given using the delay as the main parameter. In particular, we show that the positive equilibrium may switch stability at some critical delay value where a Hopf bifurcation occurs. However, this does not lead to destabilization of the system since the stability of the positive equilibrium is passed on to the limit cycle that is created via the Hopf bifurcation. In other words, the introduction of stage structure on the IG prey population enhances the species coexistence through the emergence of limit cycles.
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Acknowledgements
JAC is grateful to the IMU-CDC for the Abel Visiting Scholars Program grant and to Prof. Felicia Maria G. Magpantay for hosting him at the University of Manitoba in Fall 2016. JAC also acknowledges the support of the University of the Philippines Baguio. FMGM is grateful to NSERC Canada Discovery Grants.
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Collera, J.A., Magpantay, F.M.G. (2018). Dynamics of a Stage Structured Intraguild Predation Model. In: Kilgour, D., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Advances in Mathematical and Statistical Methods . AMMCS 2017. Springer Proceedings in Mathematics & Statistics, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-319-99719-3_30
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