Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System | Zendy

Xia Liu | Zendy; Yanwei Liu | Zendy; Jinling Wang | Zendy

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Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System

Author(s) -

Xia Liu,

Yanwei Liu,

Jinling Wang

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/898015

Subject(s) - mathematics , singularity , functional response , bifurcation , constant (computer programming) , predation , predator , mathematical analysis , control theory (sociology) , nonlinear system , physics , computer science , control (management) , quantum mechanics , biology , programming language , paleontology , artificial intelligence

A delayed predator prey system with refuge and constant rate harvesting is discussed by applying the normal form theory of retarded functional differential equations introduced by Faria and Magalhães. The analysis results show that under some conditions the system has a Bogdanov-Takens singularity. A versal unfolding of the system at this singularity is obtained. Our main results illustrate that the delay has an important effect on the dynamical behaviors of the system

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