Dynamic Analysis of Genetic Regulatory Networks with Delays

Abstract

Many biological systems have the conspicuous property to present more than one stable state and diverse rhythmic behaviors. A closed relationship has been witnessed by the pioneering works between these complex dynamic behaviors and cyclic genetic structures. This chapter analyzes the stability and bifurcation criteria of cyclic genetic regulatory networks with time delays. Not only the single cyclic genetic regulatory network but also a typical coupled cyclic genetic regulatory network through direct communication mechanism are introduced to enlighten further the dynamical evolution of living things.