Switching between oscillations and homeostasis in competing negative and positive feedback motifs

► Motifs with a positive feedback in a three-node negative feedback loop studied. ► A fixed point and a limit cycle can stably coexist in a certain parameter region. ► At the bifurcation point the period of the oscillations diverges. ► Intrinsic noise causes switching between oscillatory state and stationary state. ► Switching occurs in circadian clock models with positive and negative feedbacks.