Dynamics and bifurcations in genetic circuits with fibration symmetries.

Circuit building blocks of gene regulatory networks (GRN) have been identified through the fibration symmetries of the underlying biological graph. Here, we analyse analytically six of these circuits that occur as functional and synchronous building blocks in these networks. Of these, the lock-on, toggle switch, Smolen oscillator, feed-forward fibre and Fibonacci fibre circuits occur in living organisms, notably