Repressilator — Three-Gene Ring Oscillator (2D)

This 2D companion to the 3D single-gene Goodwin oscillator implements a genuinely different genetic-clock topology: the repressilator, in which three separate genes repress one another in a closed ring (A ⊣ B ⊣ C ⊣ A) instead of one gene repressing itself. Each gene's mRNA and protein are integrated as a real coupled ODE pair with a Hill-function repression term, exactly as in Elowitz & Leibler's original 2000 model, and the ring diagram plus a scrolling oscilloscope trace show the three proteins locking into a 120°-phase-shifted limit cycle once Hill cooperativity crosses the ring's own — much lower — bifurcation threshold. Tune cooperativity, leaky expression, transcription rate and the protein/mRNA decay ratio to see the period and phase relationships respond exactly as they do in the real synthetic-biology construct.