| R~3中的一类拟齐次向量场的性质 |
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| 引用本文： | 赵元,冯光庭,张兴安.R~3中的一类拟齐次向量场的性质[J].生物数学学报,2012(2):302-310. |
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| 作者姓名： | 赵元 冯光庭 张兴安 |
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| 作者单位： | [1]华中师范大学数学与统计学学院,湖北武汉430079 [2]湖北第二师范学院数学与数量经济学院,湖北武汉430205 |
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| 基金项目： | 国家自然科学基金（No.10771081）;湖北省教育厅科学技术重点研究项目（No.D20113005） |
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| 摘 要： | 利用三维拟齐次向量场和三维齐次向量场之间的等价关系并借鉴对齐次向量场的研究方法,把齐次向量场的一些结论推广到拟齐次向量场.并运用这些理论分析了具有不同增长率的三种群竞争模型的动力学性质和生物意义,得到增长率最大的种群在此竞争系统中占优,增长率最小的种群在此竞争系统中灭绝的结论.
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| 关 键 词： | 齐次向量场 切向量场 不变锥面 拟齐次向量场 |
The Properties of a Class of Quasi-Homogeneous Vector Fields |
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| ZHAO Yuan,FENG Guang-ting,ZHANG Xing-an.The Properties of a Class of Quasi-Homogeneous Vector Fields[J].Journal of Biomathematics,2012(2):302-310. |
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| Authors: | ZHAO Yuan FENG Guang-ting ZHANG Xing-an |
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| Institution: | School of Mathematics and Statistics, Central China Normal University, Wuhan Hubei 430079 China) (2 School of Mathematics and Quantitative Economics, Hubei University of Education, Wuhan Hubei 430205 China) |
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| Abstract: | Utilize equivalence relation between the quasi-homogeneous vector fields and the homogeneous vector fields in R3, draw lessons from the research methods of the homogeneous vector fields, and extend some conclusions on the homogeneous vector fields to the quasi-homogeneous vector fields. At last, we analyze geometrical and biological significance of three species competition model which has different growth rates, getting the largest population growth is going to survive while the smallest population growth will extinct in this comr）etition system. |
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| Keywords: | Homogeneous vector field Tangent vector field Invariant cone Quasi-homogeneous vector field |
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