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Limit cycles and singular point quantities for a 3D Lotka-Volterra system |
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| Authors: | Qinlong Wang Wentao HuangBai-Lian Li |
| Affiliation: | a School of Information and Mathematics, Yangtze University, Jingzhou 434023, PR China b Ecological Complexity and Modeling Laboratory, University of California, Riverside, CA 92521-0124, USA c School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, PR China |
| Abstract: | Four limit cycles are constructed for a three dimensional Lotka-Volterra system. This gives a good example to the cyclicity of 3D Lotka-Volterra systems. A recursion formula for computation of the singular point quantities is given for the corresponding Hopf bifurcation equation. What is worth mentioning is that the expressions of focal values are simpler, and the formula is readily done with using computer symbol operation system such as Mathematica due to its linearity. |
| Keywords: | 3D Lotka-Volterra system Hopf bifurcation Singular point quantities Center manifold |
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