JACIII Vol.27 No.3 pp. 378-385
doi: 10.20965/jaciii.2023.p0378

Research Paper:

Novel Nonlinear Control for a Class of Non-Integer Order Time Lag Gene System

Xiaoling Shi*,**,†

*Department of Mining Engineering, Luliang University
1 Xueyuan Road, Lishi District, Luiliang, Shanxi 033001, China

**School of Mechanical Engineering, North University of China
3 Xueyuan Road, Taiyuan, Shanxi 030000, China

Corresponding author

February 9, 2022
January 10, 2023
May 20, 2023
stabilization control, impulsive controller, bifurcation analysis, transcription rate

This study presents the bifurcation analysis and stabilization via the impulsive control of a fractional-order gene regulatory network with time delay. First, the author chooses the transcription rate k as the bifurcation parameter and obtains the Hopf bifurcation condition by analyzing its characteristic equation. The research shows that Hopf bifurcation occurs when the transcription rate k exceeds a critical value. This bifurcation behavior may destabilize the system. Subsequently, the author designs an impulsive controller to stabilize the system. Finally, simulation examples are used to verify our theory.

Cite this article as:
X. Shi, “Novel Nonlinear Control for a Class of Non-Integer Order Time Lag Gene System,” J. Adv. Comput. Intell. Intell. Inform., Vol.27 No.3, pp. 378-385, 2023.
Data files:
  1. [1] S. Sinha et al., “Behavior-related gene regulatory networks: A new level of organization in the brain,” Proc. of the National Academy of Sciences, Vol.117, No.38, pp. 23270-23279, 2020.
  2. [2] A. Pratapa et al., “Benchmarking algorithms for gene regulatory network inference from single-cell transcriptomic data,” Nature Methods, Vol.17, No.2, pp. 147-154, 2020.
  3. [3] X. Wang, S. Huang, and Z. Xiang, “Output feedback finite-time stabilization of a class of nonlinear time-delay systems in the p-normal form,” Int. J. of Robust and Nonlinear Control, Vol.30, No.11, pp. 4418-4432, 2020.
  4. [4] H. Li, X. Xu, and X. Ding, “Finite-time stability analysis of stochastic switched Boolean networks with impulsive effect,” Applied Mathematics and Computation, Vol.347, pp. 557-565, 2019.
  5. [5] S. Zhu, J. Lu, and Y. Liu, “Asymptotical stability of probabilistic Boolean networks with state delays,” IEEE Trans. on Automatic Control, Vol.65, No.4, pp. 1779-1784, 2019.
  6. [6] Z. Zhe et al., “A novel asymptotic stability condition for a delayed distributed order nonlinear composite system with uncertain fractional order,” J. of the Franklin Institute, Vol.359, No.18, pp. 10986-11006, 2022.
  7. [7] Z. Zhang et al., “Novel stability results of multivariable fractional-order system with time delay,” Chaos, Solitons & Fractals, Vol.157, Article No.111943, 2022.
  8. [8] E. Memlikai et al., “Design of fractional-order lead compensator for a car suspension system based on curve-fitting approximation,” Fractal and Fractional, Vol.5, No.2, Article No.46, 2021.
  9. [9] Z. Zhe et al., “Novel fractional-order decentralized control for nonlinear fractional-order composite systems with time delays,” ISA Trans., Vol.128, Part B, pp. 230-242, 2022.
  10. [10] S. Rosa and D. F. M. Torres, “Fractional-order modelling and optimal control of cholera transmission,” Fractal and Fractional, Vol.5, No.4, Article No.261, 2021.
  11. [11] Z. Zhang et al., “Novel asymptotic stability criterion for fractional-order gene regulation system with time delay,” Asian J. of Control, Vol.24, No.6, pp. 3095-3104, 2022.
  12. [12] Z. Zhe and Z. Jing, “Asymptotic stabilization of general nonlinear fractional-order systems with multiple time delays,” Nonlinear Dynamics, Vol.102, pp. 605-619, 2020.
  13. [13] C. Huang, J. Cao, and M. Xiao, “Hybrid control on bifurcation for a delayed fractional gene regulatory network,” Chaos, Solitons & Fractals, Vol.87, pp. 19-29, 2016.
  14. [14] J. H. Levine, Y. Lin, and M. B. Elowitz, “Functional roles of pulsing in genetic circuits,” Science, Vol.342, No.6163, pp. 1193-1200, 2013.
  15. [15] L. López-Maury, S. Marguerat, and J. Bähler, “Erratum: Tuning gene expression to changing environments: From rapid responses to evolutionary adaptation,” Nature Reviews Genetics, Vol.10, No.1, p. 68, 2009.
  16. [16] G. Chechik and D. Koller, “Timing of gene expression responses to environmental changes,” J. of Computational Biology, Vol.16, No.2, pp. 279-290, 2009.
  17. [17] N. Yosef and A. Regev, “Impulse control: Temporal dynamics in gene transcription,” Cell, Vol.144, No.6, pp. 886-896, 2011.
  18. [18] F. Wang, Y. Yang, and M. Hu, “Asymptotic stability of delayed fractional-order neural networks with impulsive effects,” Neurocomputing, Vol.154, pp. 239-244, 2015.
  19. [19] A. Verdugo and R. Rand, “Hopf bifurcation in a DDE model of gene expression,” Communications in Nonlinear Science and Numerical Simulation, Vol.13, No.2, pp. 235-242, 2008.
  20. [20] J. K. Hale, “Theory of functional differential equations,” Springer, 1977.
  21. [21] B. D. Hassard, N. D. Kazarinoff, and Y.-H. Wan, “Theory and applications of Hopf bifurcation,” Cambridge University Press, 1981.
  22. [22] X.-X. Liu and B.-G. Xu, “Impulsive control of a class of nonlinear time-delay differential systems,” J. of South China University of Technology (Natural Science), Vol.33, No.5, pp. 11-14, 2005.
  23. [23] S. Bhalekar and V. Daftardar-Gejji, “A Predictor-corrector scheme for solving nonlinear delay differential equations of fractional order,” J. of Fractional Calculus and Applications, Vol.1, No.5, pp. 1-9, 2011.
  24. [24] Q. Sun, M. Xiao, and B. Tao, “Local bifurcation analysis of a fractional-order dynamic model of genetic regulatory networks with delays,” Neural Processing Letters, Vol.47, No.3, pp. 1285-1296, 2018.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Jun. 07, 2023