| In the biochemistry dynamics, equationis called generalized Bruslator equation. Its mechanism in reaction ishereinto A and B are original reactant, D and E are ultimate resultant, X and Y are intermediate. There is oscillation in reaction or not rely on the existence of the limit cycle on the system. Also we want to make certain the concentration valve of the original reactant for the oscillation.In paper [4], Qin Yuanxun and Zeng Xianwu had discussed the system when p equal to 2. They attained the sufficient and necessary condition of the existence, uniqueness of the limit cycle on this system. We discuss the generalized Bruslator equation. We obtain the completely qualitative behavior of the system by using the Filippov transform and a corollary of the Zhang Zhifen Theorem. Also we consider the system when the reaction is reversible and attained the sufficient and necessary condition of the existence, uniqueness of the limit cycle on the system. |
