Inherent multistability in arrays of autoinducer coupled genetic oscillators

Rhythm generation mechanisms are very important for genetic network functions as well as for the design of synthetic genetic circuits. A significant attention to date has been focused on the synchronization of communicating genetic units, which results in the production of an unified rhythm. In contrast to this we address the question: what mechanisms of intercell communication can be responsible for multirhythmicity in globally coupled genetic units? Here, we show that an autoinducer intercell communication system that provides coupling between synthetic genetic oscillators will inherently lead to multirhythmicity and the appearance of several coexisting dynamical regimes, if the time evolution of the genetic network can be split in two well-separated time scales. We investigate in detail a variety of dynamical regimes in a genetic population and show the possibility for multiple element distributions between clusters, as well as the possibility of generating complex oscillations with different return times in one limit cycle.