Improving Dynamics of the Single-Genetic Regulatory Networks with Delays via PD Controller

In this paper, the stability and Hopf bifurcations are investigated in the single-genetic regulatory networks with time delays. The total time delay is chosen as the bifurcation parameter. We can gain that the bifurcation condition for the single-genetic regulatory networks via PD controller. At last, we carry out some experiment simulations to verify the correctness of the theoretical results.

[1]  Tonghua Zhang,et al.  The stability and Hopf bifurcation analysis of a gene expression model , 2012 .

[2]  Haijun Jiang,et al.  Hopf bifurcation analysis for a model of single genetic negative feedback autoregulatory system with delay , 2013, Neurocomputing.

[3]  Min Xiao,et al.  PID control at bifurcation in a single-gene regulatory model with delays , 2017, IECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society.

[4]  Wei Xing Zheng,et al.  Hopf Bifurcation of an $(n+1)$ -Neuron Bidirectional Associative Memory Neural Network Model With Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[5]  Jianwei Shen,et al.  Oscillatory dynamics in a simple gene regulatory network mediated by small RNAs , 2009 .

[6]  Jinde Cao,et al.  Fractional-order PD control at Hopf bifurcations in a fractional-order congestion control system , 2017, Nonlinear Dynamics.

[7]  Fang-Xiang Wu,et al.  Stability and Bifurcation of Ring-Structured Genetic Regulatory Networks With Time Delays , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Richard H. Rand,et al.  Hopf bifurcation in a DDE model of gene expression , 2008 .

[9]  Jinde Cao,et al.  Fractional-order PD control at Hopf bifurcations in delayed fractional-order small-world networks , 2017, J. Frankl. Inst..

[10]  P. R. Ouyang,et al.  Position domain nonlinear PD control for contour tracking of robotic manipulator , 2018, Robotics and Computer-Integrated Manufacturing.

[11]  Jinde Cao,et al.  Bifurcation control of complex networks model via PD controller , 2016, Neurocomputing.

[12]  Zhi-Hong Guan,et al.  Stability and Bifurcation Analysis of Cyclic Genetic Regulatory Networks with Mixed Time Delays , 2015, SIAM J. Appl. Dyn. Syst..