摘要
构造了一类依赖于某一参数δ的多项式系统 ,位于此系统的向量场中的多个相邻的单重极限环可以随δ的单调变化而同时扩大 (或缩小 ) ,不过这时极限环的扩大 (或缩小 )不一定是单调的· 由于这种向量场类似于旋转向量 ,故称此系统的这些极限环关于δ形成“类旋转向量场” ,它们可以作为研究重环和分界线环分支的一种有效工具·
A class of polynomial system was structured, which depends on a parameter δ . When δ monotonous changes, more than one neighbouring limit cycles located in the vector field of this polynomial system can expand (or reduce) together with the δ. But the expansion (or reduction) of these limit cycles is not surely monotonous. This vector field is like the rotated vector field. So these limit cycles of the polynomial system are called to constitute an “analogue rotated vector field” with δ . They may become an effective tool to study the bifurcation of multiple limit cycle or fine separatrix cycle.
出处
《应用数学和力学》
EI
CSCD
北大核心
2000年第5期541-546,共6页
Applied Mathematics and Mechanics
