Article citationsMore>>

Blé, G., Castellanos, V. and Llibre, J. (2016) Existence of Limit Cycles in a Tritrophic Food Chain Model with Holling Functional Responses of Type II and III. Mathematical Methods in the Applied Sciences, 39, 3996-4006.
https://doi.org/10.1002/mma.3842

has been cited by the following article:

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

  AUTHORS: Francisco Eduardo Castillo-Santos, Miguel Angel Dela Rosa, Iván Loreto-Hernández

  KEYWORDS: Hopf’s Bifurcation, Limit Cycle, Intraguild Model

  JOURNAL NAME: Applied Mathematics, Vol.8 No.3, March 27, 2017

  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.