Limit Cycle of Simple Chemical Reaction Systems

This paper, on the basis of authors paper[2], Studies further thesystem
$\left\{ {_{\frac{{{\rm{dy}}}}{{{\rm{dt}}}}{\rm{=a - }}{{\rm{x}}^{\rm{2}}}{\rm{y}}}^{\frac{{{\rm{dx}}}}{{{\rm{dt}}}}{\rm{=b - }}{{\rm{x}}^{\rm{2}}}{\rm{y}}}} \right.\;\;\;\;\;\;\;(1)$and a result is abtained that if a - b ≤ (a + b)³ holds, system (1) has no limit cycle.It also points out the position of limit cycles of the system (1) when a-b>(a + b)3 holds how it changes with the parameters a, b.