摘要
本文研究一类与厌氧消化过程微生物生态模型有关的微分方程组在非双曲情形下的扰动．在其一维不变流形上讨论自治扰动下中心附近发生的Ｐｉｏｎｃａｒｅ分岔，所涉及的闭轨存在性问题是许多熟知结果［１－５］不能包含的情形．进而，利用 Ｍｅｌｎｉｋｏｖ函数方法，给出周期扰动下发生次调和分岔的参数条件．
A system of differential equations related to an ecological model of perturbed microbes in anaerobic digestion process is studied. On its one dimensional invarant mani- fold,we discuss the Pioncare bifurcation near the center, the case of which is not included in known results[1-5] on existence of closed orbits. Furthermore, by use of Melnikov method we obtain the condition of parameters under which subharmomic bifurcations occur.
出处
《应用数学学报》
CSCD
北大核心
2001年第4期509-521,共13页
Acta Mathematicae Applicatae Sinica
