Abstract
The bifurcation diagram of a model nonlinear Langevin equation appropriate for delayed feedback loops in regulatory networks is obtained. We show that under parametric fluctuation the bifurcation remains sharp, both in the ranges of direct and oscillatory bifurcation. At threshold, the stationary distribution function becomes a power law in the dynamical variable. The combined effect of delay and stochasticity leads to a shift in the location of the bifurcation threshold relative to the deterministic limit of no fluctuation. The shift scales linearly with the noise intensity.
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