一类一级饱和多分子反应模型的极限环与分支

On the limit cycle and bifurcation for a one order saturated reaction model

对以生化反应为机理为背景的一类平面系统x=x（1＋y）（c－b-yn），y=（1十y）（b＋yn）－ay，这里a＞0，b≥0，c＞0，n为正整数，x≥0和y≥0进行了定性分析，研究了极限环的不存在性、存在性以及极限环唯一性和同宿轨道的存在性；改进和推广了文献[3]中的结果．

In this paper, we study a plannar system with biochemistry reaction functional background: x=x(1+Y)(c-b-yn),y=x(1+y) (b+yn) - ay, Where a >0,b≥0, c >0, n is integer(n >0 ), x >0 and y > 0, obtain the conditions of the nonexistence, existence and uniqueness for limit cycle and the uniqueness for limit cycle of the upper system is completely solved and the results in [3] are generalized and improved.