Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 51, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2019.102974
Keywords
Intraguild predation model; Predator interference; Hopf bifurcation; zero-Hopf bifurcation; Alternative stable state
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Funding
- PAPIIT, Mexico [IN116018]
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The aim of this paper is to analyze general dynamics features of a new Intraguild Predation (IGP) model where the top predator feeds only on the mesopredator and also affects its consumption rate. Important dynamical aspects of the model are described. Specifically, we prove that the trajectories of the associated system are bounded and defined for all positive time; there is a trapping domain; there are open subsets of parameters, such that the system in the first octant has at most five equilibrium solutions and at most three of them are of co-existence. Here we characterize the existence of Hopf bifurcations and we prove that this model exhibits either one, two or three small amplitude periodic solutions which arise from a zero-Hopf bifurcation. We prove the existence of alternative stable states. Finally, some numerical computations have been given in order to support our analytical results. The importance of some parameters of the model is discussed, in particular the role of the interference rate. The numerical exploration suggests that the equilibrium biomass of each of the three species grows as the level of interference grows. (C) 2019 Published by Elsevier Ltd.
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