Existence of a Limit Cycle in an Intraguild Food Web Model with Holling Type II and Logistic Growth for the Common Prey

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DOI: 10.4236/am.2017.83030    523 Downloads   677 Views  

ABSTRACT

In this paper, we prove the existence of a limit cycle for a given system of differential equations corresponding to an asymmetrical intraguild food web model with functional responses Holling type II for the middle and top predators and logistic grow for the (common) prey. The existence of such limit cycle is guaranteed, via the first Lyapunov coefficient and the Andronov-Hopf bifurcation theorem, under certain conditions for the parameters involved in the system.

Cite this paper

Castillo-Santos, F. , Rosa, M. and Loreto-Hernández, I. (2017) Existence of a Limit Cycle in an Intraguild Food Web Model with Holling Type II and Logistic Growth for the Common Prey. Applied Mathematics, 8, 358-376. doi: 10.4236/am.2017.83030.

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