BIOCOMP’11 Stability Analysis of Hybrid Stochastic Gene Regulatory Networks

Gene regulatory networks (GRNs) represent complex nonlinear coupled dynamical systems that models gene functions and regulations at the system level. Previous research has described GRNs as coupled nonlinear systems under parametric perturbations without considering the important aspect of stochasticity. However, a realistic model of a GRN is that of a hybrid stochastic retarded system that represents a complex nonlinear dynamical system including time-delays and Markovian jumping as well as noise fluctuations. In this paper, we interpret GRNs as hybrid stochastic retarded systems and prove their asymptotical stability. The theoretical results are elucidated in an illustrative example and thus shown how they can be applied to reverse engineering design.