一类生化反应方程的分枝

文[1]建立了一类生化反应方程E_(α,β),该文借助于计算机作了极限环的一些数值计算。[2]讨论了E_(σ,β)的极限环的不存在性,存在性和唯一性。本文弄清楚了E_(α,β)(α≥0,β>0)的各种分枝,包括高阶奇点分枝,各阶Hopf分枝,同宿轨道分枝,半稳定环分枝。如果还假定至多只有2个极限环,刚半稳定环分枝还是唯一的(详见定理A)。

一类生化反应方程解的 Hopf 分歧

讨论了一类生化反应方程的Ｈｏｐｆ分歧解的存在性和稳定性．

一类生化反应方程极限环问题的研究

采用一类生化反应方程ｄｘｄｔ＝１－ｘ２ｙ２ｄｙｄｔ＝β（ｘ２ｙ２－ｙ），ｘ≥０，ｙ≥０。

一类生化反应微分方程的定性分析

对一类生化反应模型x=δ-ax-xpyq,y=xpyq-by(δ>0,b>0,a>0,p 1,q>1)进行了研究.讨论了系统平衡点的稳定性态,对系统极限环的位置做出了估计.同时讨论了系统无环的充分条件以及极限环存在惟一性条件.

一类生化反应的定性分析

考察了一类生化反应系统各个奇点的各种分支值以及对奇点稳定性的影响 ,闭轨的不存在性 ,极限环的存在性等问题 ,得到了一系列的充分条件 ,推广了已有的结论 .

A study of nonlinear biochemical reaction model

The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （LWPM）. Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge-Kutta method of order four （RK-4）. Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.