Abstract:

 This paper and its sister paper mainly investgate a prey-predator system of holling's Ⅱ functional response with havesting term. By studying the change of relative situation of the sepdrdtrixs of two saddle points, a comparative completely qualitative concluaion is given. In this paper, we mainly analysis the existence of the limits cycles, particularly the existence of the three limits cycles.

Key words: 　ＰｒｅｙＰｒｅｄａｔｏｒｓｙｓｔｅｍ, ＱｕａｌｉｔａｔｉｖｅＡｎａｌｙｓｉｓ, ｅｐａｒａｔｒｉｘｃｙｃｌｅ, Ｈｏｐｆｂｉｆｕｒｃａｔｉｏｎ, Ｌｉｍｉｔｃｙｃｌｅ