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Bifurcation and Stability of the Steady-state Solutions for a Preadator-prey Model

LI Yan-ling

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Abstract

The thesis focuses on the bifurcation and the stability of the positive solutions of the predator-prey model of the predator which can produce restiong eggs.By using the theory of eigenvalue and local bifurcations,the bifurcation from the semi-trivial solution(θ,0)is obtained,and the bifurcation can be extended to global bifurcation.The stability of this solution is obtained by using perturbation theory of linear operators and stability theory of bifurcation solutions.

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What this paper is about

The thesis focuses on the bifurcation and the stability of the positive solutions of the predator-prey model of the predator which can produce restiong eggs.By using the theory of eigenvalue and local bifurcations,the bifurcation from the semi-trivial solution(θ,0)is obtained,and the bifurcation can be extended to global bifurcation.The stability of this solution is obtained by using perturbation theory of linear operators and stability theory of bifurcation solutions.

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Available abstract

The thesis focuses on the bifurcation and the stability of the positive solutions of the predator-prey model of the predator which can produce restiong eggs.By using the theory of eigenvalue and local bifurcations,the bifurcation from the semi-trivial solution(θ,0)is obtained,and the bifurcation can be extended to global bifurcation.The stability of this solution is obtained by using perturbation theory of linear operators and stability theory of bifurcation solutions.

Key concepts: Transcritical bifurcation, Saddle-node bifurcation, Bifurcation, Mathematics, Bifurcation theory, Bogdanov–Takens bifurcation, Homoclinic bifurcation, Bifurcation diagram

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