Geometric approach for global asymptotic stability of three species competitive Gompertz models

LU Gui-Chen; LU Zheng-Yi

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Geometric approach for global asymptotic stability of three species competitive Gompertz models

LU Gui-Chen 1, LU Zheng-Yi 2 *

1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China

2. Institute of Computer Applications, Academia Sinica, Chengdu 610041, China

*Correspondence author

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Funding: The Scientific Research Foundation of CQUT （No.2012ZD37）, Specialized Research Fund for the Doctoral Program of Higher Education of China （No.20115134110001）, Scientific and Technological Research Program of Chongqing Municipal Education Commission （No.KJ1400937）, The National Natural Science Foundation of Chongqing CSTC （No.cstc2014jcyjA0080）, Partially Supported by National Natural Science Foundation of China （No.11401062）

Opened online: 7 January 2015

Accepted by: none

Citation: LU Gui-Chen, LU Zheng-Yi.Geometric approach for global asymptotic stability of three species competitive Gompertz models[OL]. [ 7 January 2015] http://en.paper.edu.cn/en_releasepaper/content/4626235

This paper deals with the three dimensional competing models with Gompertz growth in biological control, by using the geometric criterion developed by Li and Muldowney and time average property to Gompertz models, some results for the global asymptotical stability of the models are obtained. Furthermore, we have investigated some open problems proposed by Jiang, Niu and Zhu, according to their classification, we have shown that classes 29 and 31 have no periodic orbit, and the interior equilibrium is global asymptotic stability.

Keywords:Gompertz model; Classification; Li-Muldowney criteria; Global asymptotic stability

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