Stability analysis for a mathematical model of the lac operon

被引：17

作者：

Mahaffy, JM ^{[1
]}

Savev, ES ^{[1
]}

机构：

[1] San Diego State Univ, Dept Math Sci, San Diego, CA 92182 USA

来源：

QUARTERLY OF APPLIED MATHEMATICS | 1999年 / 57卷 / 01期

关键词：

lac operon; induction; Hopf bifurcation; delay differential equation; global asymptotic stability; stability switches;

D O I：

10.1090/qam/1672171

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A mathematical model for induction of the lac operon is derived using biochemical kinetics and includes delays for transcription and translation, Local analysis of the unique equilibrium of this nonlinear model provides conditions for stability. Techniques are developed to determine Hopf bifurcations, and stability switching is found for the delayed system. Near a double bifurcation point a hysteresis of solutions to two stable periodic orbits is studied. Global analysis provides conditions on the model for asymptotic stability. The biological significance of our results is discussed.

引用

页码：37 / 53

页数：17

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