Bifurcation analysis in a singular Beddington-DeAngelis predator-prey model with two delays and nonlinear predator harvesting | Zendy

Xin-You Meng | Zendy; Yu-QianWu | Zendy

Open Access

Bifurcation analysis in a singular Beddington-DeAngelis predator-prey model with two delays and nonlinear predator harvesting

Author(s) -

Xin-You Meng,

Yu-QianWu

Publication year - 2019

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2019133

Subject(s) - center manifold , mathematics , hopf bifurcation , biological applications of bifurcation theory , nonlinear system , saddle node bifurcation , pitchfork bifurcation , bifurcation , control theory (sociology) , transcendental equation , singularity , transcritical bifurcation , bogdanov–takens bifurcation , mathematical analysis , differential equation , computer science , physics , control (management) , quantum mechanics , artificial intelligence

In this paper, a differential algebraic predator-prey model including two delays, Beddington-DeAngelis functional response and nonlinear predator harvesting is proposed. Without considering time delay, the existence of singularity induced bifurcation is analyzed by regarding economic interest as bifurcation parameter. In order to remove singularity induced bifurcation and stabilize the proposed system, state feedback controllers are designed in the case of zero and positive economic interest respectively. By the corresponding characteristic transcendental equation, the local stability of interior equilibrium and existence of Hopf bifurcation are discussed in the different case of two delays. By using normal form theory and center manifold theorem, properties of Hopf bifurcation are investigated. Numerical simulations are given to demonstrate our theoretical results.

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