徐州师范大学学报（自然科学版）
徐州師範大學學報（自然科學版）
서주사범대학학보（자연과학판）
JOURNAL OF XUZHOU NORMAL UNIVERSITY(NATURAL SCIENCE EDITION)
2008年
2期
101-106
,共6页
三次系统%同宿环%异宿环%极限环
三次繫統%同宿環%異宿環%極限環
삼차계통%동숙배%이숙배%겁한배
cubic system%homoclinic cycle%heteroclinic cycle%limit cycle
通过分析一类三次系统的不变三次代数曲线的性质,得出该三次曲线及一条不变直线能同时构成系统同宿环和异宿环,进而构造双参数的旋转向量场使同异宿环各自破裂而产生极限环.
通過分析一類三次繫統的不變三次代數麯線的性質,得齣該三次麯線及一條不變直線能同時構成繫統同宿環和異宿環,進而構造雙參數的鏇轉嚮量場使同異宿環各自破裂而產生極限環.
통과분석일류삼차계통적불변삼차대수곡선적성질,득출해삼차곡선급일조불변직선능동시구성계통동숙배화이숙배,진이구조쌍삼수적선전향량장사동이숙배각자파렬이산생겁한배.
An invariant cubic curve of a cubic system is first presented in this paper. By studying the properties of the invariant curve in detail, it is concluded that the invariant cubic curve together with an invariant line can constitute a homoclinic cycle and a heteroclinic cycle of the cubic system, which has not been seen before. Finally, a two-parameter rotated vector field is constructed to bifurcate limit cycles from the homoclinic and heteroclinic cycles, respectively.
