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2002•Journal of Central China Normal UniversityRequires access

Bifurcations in a predator-prey system with Holling type-IV functional response

Huang Ji

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Abstract

In this paper, a predator prey system with Holling type IV functional response:p(x)=xa+bx+x 2 is considered. Bifurcations analysis of the mode is carried out as b0. The bifurcation analysis of the model depending on all parameters indicates that it exhibits numerous kinds of bifurcation phenomena including the saddle node bifurcation, the Hopf bifurcation and the homoclinic bifurcation etc. In the generic case, the model has the cusp bifurcation of codimension 2 (i.e. Bogdanov Takens bifurcation).

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What this paper is about

In this paper, a predator prey system with Holling type IV functional response:p(x)=xa+bx+x 2 is considered. Bifurcations analysis of the mode is carried out as b0. The bifurcation analysis of the model depending on all parameters indicates that it exhibits numerous kinds of bifurcation phenomena including the saddle node bifurcation, the Hopf bifurcation and the homoclinic bifurcation etc. In the generic case, the model has the cusp bifurcation of codimension 2 (i.e. Bogdanov Takens bifurcation).

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Available abstract

In this paper, a predator prey system with Holling type IV functional response:p(x)=xa+bx+x 2 is considered. Bifurcations analysis of the mode is carried out as b0. The bifurcation analysis of the model depending on all parameters indicates that it exhibits numerous kinds of bifurcation phenomena including the saddle node bifurcation, the Hopf bifurcation and the homoclinic bifurcation etc. In the generic case, the model has the cusp bifurcation of codimension 2 (i.e. Bogdanov Takens bifurcation).

Key concepts: Bogdanov–Takens bifurcation, Saddle-node bifurcation, Homoclinic bifurcation, Bifurcation, Mathematics, Functional response, Transcritical bifurcation, Biological applications of bifurcation theory

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