The qualitative behavior of the system at the origin in the interior of the first quadrant is studied 对系统在原点的性态,我们作了全面的分析。
In the cases of and , there has no closed orbit to the system ( * ) in the first quadrant 这里,为某一负值, 。对和不定号的情形,系统( * )在第一象限内均不存在极限环。
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 我们得到下列结论:定理1 、当时,系统( * )在第一象限内至少存在一个极限环;定理2 、当时,系统( * )在第一象限内至多存在一个极限环,若存在必为稳定的;定理3 、当时,系统( * )在第一象限内存在唯一的极限环,且为稳定的。