Before revision:  Despite numerous experimental works supporting evidence of hysteresis in gene regulatory networks , such phenomenon may not be compatible with the stochasticityunderlying gene regulation dynamics. Here we show how under sufficiently slow dynamics, the dependency of the transient solutions on the initial state of the cells can be mistakenly interpreted as hysteresis and, to quantify this phenomenon, we provide an estimate of the convergence rate to the equilibrium.
After revision:  Despite numerous experimental works supporting evidence of hysteresis in gene regulatory networks with their inherent stochasticity. Under sufficiently slow dynamics, the dependency of the transient solutions on the initial state of the cells can be mistakenly interpreted as hysteresis and, to quantify this phenomenon, we provide an estimate of the convergence rate to the equilibrium.