Qualitative Analysis and Numerical Simulation of Positive Solutions for a Predator-Prey Model
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Qualitative Analysis and Numerical Simulation of Positive Solutions for a Predator-Prey Model
Acta Scientiarum Naturalium Universitatis SunYatseniVol. 54, Issue 4, Pages: 55-62(2015)
作者机构:
宝鸡文理学院数学与信息科学学院,陕西,宝鸡,721013
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Published:2015,
Published Online:25 August 2015,
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WANG Lijuan, JIANG Hongling. Qualitative Analysis and Numerical Simulation of Positive Solutions for a Predator-Prey Model. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 54(4):55-62(2015)
DOI:
WANG Lijuan, JIANG Hongling. Qualitative Analysis and Numerical Simulation of Positive Solutions for a Predator-Prey Model. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 54(4):55-62(2015)DOI:
Qualitative Analysis and Numerical Simulation of Positive Solutions for a Predator-Prey Model
The steady state positive solutions of a predator-prey model with diffusion are studied. A priori estimate for positive solutions is obtained by using maximum principle. Applying to the local bifurcation theory
the existence of local bifurcation solutions is given. It follows from the global bifurcation theory that the local bifurcation solution can be extended to global bifurcation solution and the trend is obtained. Then a necessary and sufficient condition for the existence of positive solutions is obtained. By the stability theory
the stability of local bifurcation solutions is investigated. Finally
the theoretical results are verified and complemented by the numerical simulation.