一类广义布鲁塞尔振子模型的周期轨(英文)

Periodic solutions in the generalized Brusselator

作者考虑了一类广义的布鲁塞尔振子模型.在已有的关于此系统结论的基础上,证明了在条件bp-b-1>0,(b/ap-1)1/q=abq/(bp-b-1))下,系统唯一平衡点S:(a,(b/ap-1)1/q)是一个一阶稳定的细焦点,并且一个渐近稳定的周期轨将从该处的Hopf分岔产生.这个结果对应的已有结果.此外,也给出了关于此系统的周期轨的存在性和不存在性条件.

The authors consider a kind of generalized Brusselator, a polynomial differential system of p ＋ q degree, which was given from a general multi-molecular reaction in biochemistry as a theoretical problem of concentration kinetics. Based on the known therorems on the model, they prove that the unique equilibrium S： （α, （b/α^p-l）^1/q） is a stable weak focus with multilicity 1 under conditions bp - b - 1 〉0, （b/α^p-1）^1/q= αbq/（ bp - b - 1） and a unique asymptotically stable periodic solution with small amplitude is produced from Hopf bifurcation, which correct the corresponding result obtained by Yan in 2001. Furthermore, conditions for the nonexistence and existence of periodic solutions are are also given.