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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Stability and Bifurcation Analysis of Three Species Predator-PreyModel with Holling Type II

Discontinuity, Nonlinearity, and Complexity 8(2) (2019) 127--144 | DOI:10.5890/DNC.2019.06.002

M. Sambath, C. Gokila

Department of Mathematics, Periyar University, Salem 636011, India

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Abstract

This paper considers a prey predator model with omnivore population and Holling type II response. First, we have studied the boundedness of the model system. The local and global stability of the equilibrium is investigated by analyzing the eigenvalues and constructing the appropriate Lyapunov functions respectively. The persistence of positive equilibrium is also discussed. The existence of Hopf bifurcation is investigated by analyzing the distribution of eigenvalues at the positive equilibrium point. By using the normal form theory and explicit formulae which determine the direction of bifurcating periodic solutions are derived. Some numerical simulations are carrying out, to check our theoretical results.

Acknowledgments

The work of the first author is supported by the UGC-SAP (Grant No. F.510/7/DRS1/2016 (SAP-I)) UGC, Govt. of India. And the work of second author is supported by the DST-INSPIRE Fellowship (No: DST/INSPIRE FELLOWSHIP/2017/IF170244), DST, Govt. of India.

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