Synchronized oscillations and chaos in coupled genetic repressilators

Living organisms are complex, and are typically composed of many interacting subsystems. In order to understand the complex genetic networks present in the whole cell, it is of crucial importance to first understand the dynamic behavior of modular genetic circuits. Recently a few subsystems on the genetic level, namely, genetic repressilators or oscillators, and bi-stable gene circuits, have been constructed and manipulated. In the former case, while mathematical model predicts simple oscillations, it has been observed that period varies from one oscillation to another considerably. Realizing that laboratory biochemical experiments take place in space in a distributed way, we study coupled repressilators. Let the repressilator of Elowitz and Leibler [1] be described by the following set of 6 ordinary differential equations: