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Multiple limit cycles for three-dimensional Lotka-Volterra systems
LUO Yong 1, LU Gui-Chen 2, LU Zheng-Yi 3 *
1. College of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035
2. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China
3. Institute of Computer Applications, Academia Sinica, Chengdu 610041, China
*Correspondence author
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Funding: Partially Supported by the National Natural Science Foundation of China (No.11001204), the National Natural Science Foundation of China (No.11401062), Scientific and Technological Research Program of Chongqing Municipal Education Commission (No.KJ1400937), the National Natural Science Foundation of Chongqing CSTC (No.cstc2014jcyjA0080), The Scientific Research Foundation of CQUT (No.2012ZD37), Specialized Research Fund for the Doctoral Program of Higher Education of China (No.20115134110001)
Opened online: 7 January 2015
Accepted by: none
Citation: LUO Yong, LU Gui-Chen, LU Zheng-Yi.Multiple limit cycles for three-dimensional Lotka-Volterra systems[OL]. [ 7 January 2015] http://en.paper.edu.cn/en_releasepaper/content/4626241
 
 
Multiple limit cycles are shown to appear in three-dimensional Lotka-Volterra systems with various types of interactions formed by mutualism, competition and prey-predator. In this paper, under the density dependance and the nonzero off-diagonal elements of interaction matrix, we classify the three-dimensional Lotka-Volterra systems into ten classes and show that besides the known results for classes 2, 3, 5 and 9, in each class of the remaining six ones, a corresponding system can be constructed to have at least two or three limit cycles based on an algorithmic construction method proposed by Hofbauer and So with a modification of Lu and Luo.
Keywords:Lotka-Volterra systems, 3D-classification, Center manifold, Hopf bifurcation, Multiple limit cycles
 
 
 

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