title: Stability and bifurcation analysis of new coupled repressilators in genetic regulatory networks with delays.
abstract: The genetic regulatory networks are complex dynamic systems which reflect various kinetic behaviors of living things. In this paper, a new structure of coupled repressilators is introduced to exploit the underlying functions. The new coupled repressilator model consists of two identical repressilators inhibiting each other directly. The coupling delays are taken into account. The existence of a unique equilibrium for this system is verified firstly, then the stability criteria for equilibrium are analyzed without and with coupling delays. The different functions on equilibrium and its stability played by related biochemical parameters in the structure including maximal transcription rate, coupling strength, the decay rate ratio between proteins and mRNAs, and coupling delays are discussed. At last, several numerical simulations are made to demonstrate our results.
authors.affiliation: College of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; School of Science, Tianjin University of Technology and Education, Tianjin 300222, China.
authors.forename: Guang
authors.initials: G
authors.lastname: Ling
authors.affiliation: College of Automation, Huazhong University of Science and Technology, Wuhan 430074, China. Electronic address: zhguan@mail.hust.edu.cn.
authors.forename: Zhi-Hong
authors.initials: ZH
authors.lastname: Guan
authors.affiliation: College of Automation, Huazhong University of Science and Technology, Wuhan 430074, China. Electronic address: hedingxin@mail.hust.edu.cn.
authors.forename: Ding-Xin
authors.initials: DX
authors.lastname: He
authors.affiliation: Petroleum Engineering College, Yangtze University, Jingzhou 420400, China.
authors.forename: Rui-Quan
authors.initials: RQ
authors.lastname: Liao
authors.affiliation: College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi 435002, China.
authors.forename: Xian-He
authors.initials: XH
authors.lastname: Zhang
mesh_terms: D053263:Gene Regulatory Networks; D007700:Kinetics; D008957:Models, Genetic; D014158:Transcription, Genetic
keywords: Coupled repressilators; Coupling delays; Hopf bifurcation; Stability