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Single-cell stochastic gene expression, with gene state switching, transcription, translation, and negative feedback, can exhibit oscillatory kinetics that is statistically characterized in terms of a non-monotonic power spectrum. Using a solvable model, we illustrate the oscillation as a stochastic circulation along a hysteresis loop. A triphasic bifurcation upon the increasing strength of negative feedback is observed, which reveals how random bursts evolve into stochastic oscillations.arXiv:1909.09769v1 fatcat:z3k4f367ebfefmif4avcl4qotu