Robust stability analysis of multi-time scale genetic regulatory networks under parametric uncertainties.

Genetic regulatory networks are prone to internal parametrical fluctuations as well as external noises and are modeled as multi-time scale systems with time-delay. Robustness represents a crucial property of these networks to attenuate the effects of internal fluctuations and external noise. In this study, we formulate biological networks as coupled nonlinear differential systems operating at different time-scales under consideration of time delay and vanishing perturbations. We determine conditions for the existence of a global uniform attractor of the perturbed biological system. By using a Lyapunov function for the coupled system, we derive a maximal upper bound for the fast time scale associated with the fast state