The qualitative behavior of the system at the origin in the interior of the first quadrant is studied 對系統在原點的性態,我們作了全面的分析。
In the cases of and , there has no closed orbit to the system ( * ) in the first quadrant 這里,為某一負值, 。對和不定號的情形,系統( * )在第一象限內均不存在極限環。
When , there exists at least one limit cycle to the system ( * ) in the first quadrant ; theorem 2 . when , there exsits at most one limit cycle to the system ( * ) in the first quadrant ; theorem 3 . when , there exactly exists one limit cycle to the system ( * ) in the first quadrant 我們得到下列結論:定理1 、當時,系統( * )在第一象限內至少存在一個極限環;定理2 、當時,系統( * )在第一象限內至多存在一個極限環,若存在必為穩定的;定理3 、當時,系統( * )在第一象限內存在唯一的極限環,且為穩定的。