File:Robust Stability of Genetic Regulatory Networks with Stochastic Time Delays Under Intrinsic and Extrinsic Noise.pdf

Noise is ubiquitous in gene expression and genetic regulatory networks are formulated as nonlinear stochastic differential equations with time delays. Both intrinsic and extrinsic noises are considered in this formulation to model the uncertainty and fluctuation of kinetic parameters and time delays. A novel Lyapunov - Krasovskii functional has been proposed using the stochastic analysis approach. The theorem is formulated in the form of Linear Matrix Inequality.