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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Hopf Bifurcation and Stability Analysis of a Predator-Prey System with Holling Type IV Functional Response

Journal of Applied Nonlinear Dynamics 7(4) (2018) 337--348 | DOI:10.5890/JAND.2018.12.002

Z. Lajmiri$^{1}$, R. Khoshsiar Ghaziani$^{2}$, I. Orak$^{1}$

$^{1}$ Sama technical and vocational training college, Islamic Azad University , Izeh branch, Izeh Iran

$^{2}$ Department of Applied Mathematics, Shahrekord University, P.O.Box. 115, Shahrekord, Iran

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Abstract

In this paper, we investigate the dynamical complexities of a predator-prey model with Holling type IV functional response, which describes interaction between two populations of prey and predator. We perform a bifurcation analysis of this model analytically and numerically. Our bifurcation analysis indicates that the system exhibits numerous types of codimension one and two bifurcations including fold, subcritical and supercritical Hopf, cusp and Bogdanov-Takens. By numerical continuation method, we also compute several curves of equilibria and bifurcations. Further, by numerical simulations we reveal more complex dynamics of the model.

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