一类多分子反应模型的闭轨的存在性  

Existence of Closed Orbits for a Model Concerning Multimolecule Reactions

作　　者：董士杰[1] 徐瑞[1] 

机构地区：[1]军械工程学院数学教研室

出　　处：《工程数学学报》1999年第1期59-63,26,共6页Chinese Journal of Engineering Mathematics

摘　　要：研究了一类多分子反应模型ｄｘｄｔ＝１－ｘｐｙ３ｄｙｄｔ＝α（ｘｐｙ３－ｙ）（α＞０，ｐ∈Ｎ）的闭轨的存在性。结论是，存在α＊∈ｐ２，α０，使当ｐ２＜α＜α＊时，该系统有稳定的极限环；当α＞α０或０＜α＜α１＜ｐ２时，该系统没有极限环，其中α０，α１与α＊的表达式见正文。Abstract The existance of closed orbits for the biochemical reaction model: d x d t=1-x py 3 d y d t=α(x py 3-y) (α>0,p∈N) is discussed. By using the gualitative theory of ordinary differential equations, the following results are obtained: there exists a constant α *∈p2,α 0 such that if α∈p2,α * , then system has at least one stable limit cycle; if α>α 0 or 0<α<α 1 then system has no limit cycle, where α 0=p212p+2 p+2p -2p+2 2p +1 3p α 1=4p p+3 (p-1) p+2 (p+5) p+5 (p+2) p+2 (5p-2) p+5 1p

关 键 词：闭轨 极限环 细焦点 多分子反应模型 存在性 

分 类 号：O175.12[理学—数学] O643.1[理学—基础数学]