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Bogdanov-Takens Bifurcation in a Leslie-Gower Predator-prey Model with Prey Harvesting

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Acta Mathematicae Applicatae Sinica 2014年第1期30卷 239-244页

作者： Yi-jun GONG Ji-cai HUANG School of Mathematics and Statistics Central China Normal University

This paper discuss the cusp bifurcation of codimension 2 （i.e. Bogdanov-Takens bifurcation） in a Leslie^Gower predator-prey model with prey harvesting, which was not revealed by Zhu and Lan [Phase portraits, Hopf bifurcation and limit cycles of Leslie-Gower predator-prey systems with harvesting rates, Discrete and Continuous Dynamical Systems Series B. 14（1）（2010）, 289-306]. It is shown that there are different parameter values for which the model has a limit cycle or a homoclinic loop.

关键词： Leslie-Gower predator-prey model Bogdanov-Takens bifurcation limit cycle homoclinic loop

BIFURCATIONS OF A CUBIC SYSTEM PERTURBED BY DEGREE FIVE

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Acta Mathematica Scientia 2009年第1期29卷 11-24页

作者：尚德生张同华 School of Mathematics and Information Science Shandong University of Technology Department of Chemical Engineering Curtin University of Technology

In this article, using multi-parameter perturbation theory and qualitative analysis, the authors studied a kind of cubic system perturbed by degree five and ob-tained the system that can have 17 limit cycles giving th... 详细信息

关键词： Perturbation singular point value homoclinic loop limit cycle

The Global Bifurcation of a Cubic System

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Acta Mathematicae Applicatae Sinica 2006年第2期22卷 325-332页

作者： De-sheng Shang Mao-an Han Jin-ping Sun School of Mathematics and Information Science Shandong University of Technology Zibo 255049 China School of Mathematical Sciences Shanghai Normal University Shanghai 200234 China

In this paper, we study the perturbation of certain of cubic system. By using the method of multi-parameter perturbation theory and qualitative analysis, we infer that the system under consideration can have five limi... 详细信息

关键词： Perturbation bifurcation cubic system limit cycle homoclinic loop

LIMIT CYCLES OF A QUADRATIC HAMILTONIAN SYSTEM BY CUBIC PERTURBATIONS

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Annals of Differential Equations 2007年第4期23卷 593-602页

作者： Zhao Yong Han Maoan Yang Junmin Institute of Math. Shanghai Normal University Shanghai 200234

In this paper, we are concerned with a cubic near-Hamiltonian system, whose unperturbed system is quadratic and has a symmetric homoclinic loop. By using the method developed in [12], we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop. Further, we give a condition under which there exist 4 limit cycles.

关键词： limit cycles homoclinic loop near-Hamiltonian systems cubic perturbations Melnikov method