Sliding Bifurcation Analysis and Global Dynamics for a Filippov Predator-prey System | Zendy

Xuewen Tan | Zendy; Wenjie Qin | Zendy; Xinzhi Liu | Zendy; Jin Yang | Zendy; Shaoping Jiang | Zendy

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Sliding Bifurcation Analysis and Global Dynamics for a Filippov Predator-prey System

Author(s) -

Xuewen Tan,

Wenjie Qin,

Xinzhi Liu,

Jin Yang,

Shaoping Jiang

Publication year - 2016

Publication title -

the journal of nonlinear sciences and applications

Language(s) - English

Resource type - Journals

eISSN - 2008-1901

pISSN - 2008-1898

DOI - 10.22436/jnsa.009.06.42

Subject(s) - mathematics , predation , control theory (sociology) , bifurcation , dynamics (music) , predator , nonlinear system , computer science , ecology , biology , artificial intelligence , control (management) , physics , quantum mechanics , acoustics

This paper studies a Filippov predator-prey system, where chemical control strategies are proposed and analyzed. Initially, the exact sliding segment and its domains are addressed. Then the existence and stability of the regular, virtual, pseudo-equilibria and tangent points are discussed. It shows that two regular equilibria and a pseudo-equilibrium can coexist. By employing theoretical and numerical techniques several kinds of bifurcations are investigated, such as sliding bifurcations related to the boundary node (focus) bifurcations, touching bifurcations, sliding crossing bifurcation and buckling bifurcations (or sliding switching). Furthermore, it makes comparison of the obtained results with previous studies for the Filippov predator-prey system without control strategies. Some biological implications of our results with respect to pest control are also given. c ©2016 All rights reserved.

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