Stability and bifurcation of delay-coupled genetic regulatory networks with hub structure |
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| Authors: | Dandan Yue Zhi-Hong Guan Juan Li Feng Liu Jiang-Wen Xiao Guang Ling |
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| Institution: | 1. College of Automation, Huazhong University of Science and Technology, Wuhan 430074, PR China;2. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, PR China;3. School of Automation, China University of Geosciences, Wuhan 430074, PR China;4. School of Science, Wuhan University of Technology, Wuhan 430074, PR China |
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| Abstract: | In this paper, we study the local stability and bifurcation of a delay-coupled genetic regulatory networks consisting of two modes with the hub structure. By analyzing the equilibrium equation, the number of the positive equilibria is discussed in both the cases that there are inhibition coupling and activation coupling in the networks. It is revealed that multiple equilibria could exist in the developed genetic networks and the number of the equilibria could be distinct under the two cases of delayed-coupling. For the equilibrium, the conditions of the coupling-delay-independent stability and the saddle-node bifurcation are derived with respect to the biochemical parameters. The coupling-delay-dependent stability and the Hopf bifurcation criteria on the biological parameters and the coupling delay are also given. Moreover, the complexity of the algorithm used in this paper is analyzed. The numerical simulations are made to certify the obtained results. The multistability of the developed genetic regulatory networks is displayed. The different effects of the coupling delay on the stability of the genetic networks under different biochemical parameters are shown. |
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| Keywords: | Corresponding author |
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