R^3中的一类拟齐次向量场的性质

The Properties of a Class of Quasi-Homogeneous Vector Fields

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.

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.