ScholarLens Back to search
2014•微分方程年刊：英文版Requires access

BIFURCATIONS OF DEGENERATE SINGULAR POINT OF A PREDATOR-PREY SYSTEM WITH HOLLING-IV FUNCTIONAL RESPONSE

Jiangbin, Chen

Open publisher page 1 citations

Abstract

A predator-prey system with Holling-IV functional response is investigated. It is shown that the system has a positive equilibrium?which is a cusp of co-dimension 2 under certain conditions. When the parameters vary in a small neighborhood of the values of parameters, the model undergoes the Bogdanov-Takens bifurcation. Different kinds of bifurcation phenomena are exhibited, which include the saddle~node bifurcation, the Hopf bifurcation and the homo-clinic bifurcation. Some computer simulations are presented to illustrate the conclusions.

About this research paper

What this paper is about

A predator-prey system with Holling-IV functional response is investigated. It is shown that the system has a positive equilibrium?which is a cusp of co-dimension 2 under certain conditions. When the parameters vary in a small neighborhood of the values of parameters, the model undergoes the Bogdanov-Takens bifurcation. Different kinds of bifurcation phenomena are exhibited, which include the saddle~node bifurcation, the Hopf bifurcation and the homo-clinic bifurcation. Some computer simulations are presented to illustrate the conclusions.

Why it matters

OpenAlex reports 1 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

A predator-prey system with Holling-IV functional response is investigated. It is shown that the system has a positive equilibrium?which is a cusp of co-dimension 2 under certain conditions. When the parameters vary in a small neighborhood of the values of parameters, the model undergoes the Bogdanov-Takens bifurcation. Different kinds of bifurcation phenomena are exhibited, which include the saddle~node bifurcation, the Hopf bifurcation and the homo-clinic bifurcation. Some computer simulations are presented to illustrate the conclusions.

Key concepts: Bogdanov–Takens bifurcation, Functional response, Saddle-node bifurcation, Bifurcation, Mathematics, Cusp (singularity), Degenerate energy levels, Pitchfork bifurcation

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
BIFURCATIONS OF DEGENERATE SINGULAR POINT OF A PREDATOR-PREY SYSTEM WITH HOLLING-IV FUNCTIONAL RESPONSE — Research Paper | ScholarLens