Hopf Bifurcation Analysis of the Repressilator Model

• 作者: Anael Verdugo
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: HOPF BIFURCATION Repressilator CENTER MANIFOLD ANALYSIS
• 年，卷（期）: 2018,（2）
• 页码范围: 137-152
• 页数: 16页
• 分类号: O1

摘要

The repressilator is a genetic network that exhibits oscillations. The net-work is formed of three genes, each of which represses each other cyclically, creating a negative feedback loop with nonlinear interactions. In this work we present a computational bifurcation analysis of the mathematical model of the repressilator. We show that the steady state undergoes a transition from stable to unstable giving rise to a stable limit-cycle in a Hopf bifurcation. The nonlinear analysis involves a center manifold reduction on the six-dimensional system, which yields closed form expressions for the frequency and amplitude of the oscillation born at the Hopf. A parameter study then shows how the dynamics of the system are influenced for different parameter values and their associated biological significance.