Chaotic Dynamics in a Tryptophan Repressible Operon Model

摘要

A repressor-mediated repression process, often observed in bacteria, is modelled using a gene enzyme-end-product control unit. In this paper, we study a periodically driven repressible tryptophan operon model describing such a process. We find that, when unperturbed, our model typically possesses a 3-dimensional limit cycle, which is a global attractor, for all initial conditions of the system. However, under the effect of external periodic forcing, this simple periodic behavior becomes considerably more complex, as the limit cycle turns to a strange attractor, with a broadband spectrum, positive largest Lyapunov exponent, and a non integer fractal dimension, displaying chaotic dynamics in its vicinity.