Author(s)

Anael Verdugo^1,2

¹Department of Mathematics, California State University, Fullerton, CA, USA.
²Center for Computational and Applied Mathematics, California State University, Fullerton, CA, USA.

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.

Hopf Bifurcation, Repressilator, Center Manifold Analysis

Verdugo, A. (2018) Hopf Bifurcation Analysis of the Repressilator Model. American Journal of Computational Mathematics, 8, 137-152. doi: 10.4236/ajcm.2018.82011.