Stochastic stability analysis of gene regulatory networks using hybrid systems theory

Upon the completion of the sequencing of the human genome, an urgent need emerged to develop tools capable of unraveling the interaction and functionality of genes. With the aid of microarray technology, large scale gene expression analyses have been conducted and several gene regulatory network models have been proposed. To establish a framework that better integrates and regulates such models, the stochastic stability properties of these models have to be defined and investigated. Such a study would uncover regimes of stable behavior under both intrinsic and extrinsic noise as well as random changes in model parameters due to abruptly changing environment conditions. In this article, stochastic stability for a class of Hybrid Gene Regulatory Network (HGRN) Models is defined. A particular interest is to study and derive conditions that guarantee asymptotic exponential stochastic stability when several random switching processes are effecting the behavior of the GRN model. A numerical example is included to demonstrate the theoretical analysis.