The AC-DC Circuit Is the Combination of a Bistable Switch and a Repressilator
(A) AC-DC regulatory circuit.
(B) Bifurcation diagram and network diagram for the bistable switch controlled by a signal S. The two saddle-node bifurcations position the stability range for the two stable solutions (black solid lines). There is bistability for intermediate signals, where both stable solutions are separated by an unstable steady state (dashed line). Transient trajectories (pink arrows) are sketched showing the dynamical effect of the steady states.
(C) Bifurcation diagram and network diagram for the repressilator under a change of parameters controlled with an external signal S. The change in behavior is a Hopf bifurcation where a stable spiral (damped oscillations) (thick black solid line) becomes unstable (dashed line) giving rise to stable oscillations (shaded zone). After the bifurcation, the amplitude of the stable oscillations (delimited by thin solid lines) grows with the signal. The two possible oscillatory transients are sketched (pink arrows).