| Kopel系统的分岔研究 |
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| 引用本文： | 于晋臣,张彩艳.Kopel系统的分岔研究[J].山东交通学院学报,2009,17(2):77-81. |
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| 作者姓名： | 于晋臣 张彩艳 |
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| 作者单位： | 1. 山东交通学院,数理系,山东,济南,250023
2. 山东大学,数学学院,山东,济南,250100;山东电子职业技术学院,山东,济南,250014 |
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| 摘 要： | 应用中心流形定理和分岔理论,证明Kopel系统会发生跨临界分岔和叉式分岔.运用数值方法证明了当临界平衡点失稳时,系统中Neimark-Sacker分岔的存在,即从平衡点处会分岔出稳定的极限环.应用Matlab进行了数值模拟,数值模拟的结果与理论分析一致,而且数值分析展示了更为丰富的动力行为.
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| 关 键 词： | 跨临界分岔 叉式分岔 Neimark-Sacker分岔 |
Study of Bifurcation in Kopel System |
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| YU Jin-chen,ZHANG Cai-yan.Study of Bifurcation in Kopel System[J].JOURNAL OF SHANDONG JIAOTONG UNIVERSITY,2009,17(2):77-81. |
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| Authors: | YU Jin-chen ZHANG Cai-yan |
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| Institution: | 1.Department of Mathematics and Physics;Shandong Jiaotong University;Jinan 250023;China;2.School of Mathematics;Shandong University;Jinan 250100;3.Shandong College of Electronic Technology;Jinan 250014;China |
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| Abstract: | With the center manifold theorem and the bifurcation theory,it is proved that transctitical bifurcation and pitchfork bifurcation can appear in Kopel system.The critical equilibrium loses its stability as Neimark-Sacker bifurcation occurs,which is proved by using the numerical method.Matlab is applied to make numerical simulation,the results of which not only show the consistence with the theoretical analysis but also display richer dynamics of the system. |
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| Keywords: | transcritical bifurcation pitchfork bifurcation Neimark-Sacker bifurcation |
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